binary convexities and distributive lattices a convex structure is binary if every finite family of pairwise intersecting convex sets has a non empty intersection distributive lattices with the convexity of all order convex sublattices are a prominent type of example because they correspond exactly to the intervals of a binary convex structure which has a certain separation property in one direction this result relies on a study of so called base point orders induced by a convex structure these orderings are used to construct an intrinsic topology for binary convexities certain basic questions are answered with the aid of some results on completely distributive lattices several applications are given dimension problems are studied in a subsequent paper 0 introduction a convex structure consists of a set x together with a collection of subsets of x henceforth called convex sets such that 1 1 the empty set and the set x are convex 1 2 the intersection of convex sets is convex 1 3 the union of an updirected collection of convex sets is convex the collection itself is called a convexity on x axiom 1 2 allows the construction of an associated convex hull operator usually denoted by h in the obvious way the hull of a finite set is called a polytope and the hull of a two point set is also called an interval a half space is a convex set with a convex complement the following separation axioms comparable with the axioms tl 5 t4 in topology are used frequently sx singletons are convex which we will assume throughout s2 two distinct points are in complementary half spaces s3 a convex set is an intersection of half spaces s4 two disjoint convex sets extend to complementary half spaces in this paper we will concentrate largely on a particular though fundamental class of convexities with the following binarity property each finite collection of pairwise intersecting convex sets has a non empty intersection the basic types of examples are described in 1 many of these examples arise in a topological context for other examples a natural topology can be constructed binary convex structures on a topological space have been studied extensively in the past years 15 17 19 22 29 34 38 the topology and the convexity are always assumed to be compatible in the sense that polytopes are closed a triple consisting of a set x a convexity and a compatible topology st is called a topological convex proc london math soc 3 48 1984 1 33 5388 3 48 a

cartan decomposition subgroups of 2 for g sl 3 r and g so 2 n we give explicit practical conditions that determine whether or not a closed connected subgroup h of g has the property that there exists a compact subset c of g with chc g to do this we fix a cartan decomposition g ka k of g and then carry out an approximate calculation of khk n a for each closed connected subgroup h of g

the kakutani property and the fixed point property of topological spaces with abstract convexity abstract the paper deals with the usual fixed point property and the following kakutani property of a space x for every upper semicontinuous function from x to non empty closed convex subsets of x there exists x0 such that x0 x0 we derive this property of x from various separation properties of convex subsets of x and a kind of local convexity of x convexity in our setup is given in an abstract axiomatic way special emphasis is given to the case where x has the form of a product the obtained results cover several known fixed point theorems ky fan glicksberg wallace and special cases of eilenberg montgomery we also discuss an open problem concerning the fixed point property of finite posets and its role in proving more advanced theorems

information acquisition in auctions our aim in this paper is to study the incentives to acquire information we consider decision problems where the payoff has the single crossing property and signals are affiliated with the unknown parameter we introduce the notion of risk sensitiity and establish that the value of information is higher in decision problems that are more risk sensitive we apply this result to auctions we are able to show that a first price auction induces more information acquisition than a second price auction consider a decision maker choosing an action a to maximize the expected value of a payoff function u a the decision maker does not observe which he regards as a random variable v instead he observes the realization of a random variable x a signal which conveys information about w eassume that the decision maker can make x more informative at a cost making x more informative increases the expected payoff we analyze the returns to making x more informative we focus on problems where x and v are affiliated and u a has the weak

poincare series for non riemannian locally symmetric spaces abstract we initiate the spectral analysis of pseudo riemannian locally symmetric spaces g h beyond the classical cases where h is compact automorphic forms or is trivial analysis on symmetric spaces for any non riemannian reductive symmetric space x g h on which the discrete spectrum of the laplacian is nonempty and for any discrete group of isometries whose action on x is sufficiently proper we construct l 2 eigenfunctions of the laplacian on x x for an infinite set of eigenvalues these eigenfunctions are obtained as generalized poincare series i e as projections to x of sums over the orbits of eigenfunctions of the laplacian on x we prove that the poincare series we construct still converge and define nonzero l 2 functions after any small deformation of inside g for a large class of groups thus the infinite set of eigenvalues we construct is stable under small deformations this contrasts with the classical setting where the nonzero discrete spectrum varies on the teichmuller space of a compact riemann surface we actually construct joint l 2 eigenfunctions for the whole commutative algebra of invariant differential operators on x

on closed anti de sitter spacetimes this article deals with the structure of the fundamental group of compact anti de sitter spacetimes i e lorentz manifolds with constant negative curvature algebraically such a manifold is the quotient of the universal cover of the homogeneous space so 2 n so 1 n by a discrete group gamma acting properly and co compactly on it this exists if and only if n is even indeed as this was observed by kulkarni u 1 d is contained in so 2 2d and acts properly transitively on so 2 2d so 1 2d it then suffices to take gamma as a co compact lattice in u 1 d the results of the present article give evidence to the question in dimension 3 are all compact anti de sitter spacetimes constructed in this way

a further characteristic of abstract convexity structures on topological spaces abstract in this paper we give a characteristic of abstract convexity structures on topological spaces with selection property we show that if a convexity structure c defined on a topological space has the weak selection property then c satisfies h 0 condition moreover in a compact convex subset of a topological space with convexity structure the weak selection property implies the fixed point property

disappearance of cusp forms in special families in his 1954 g6ttingen lectures atle selberg sb posed the question of the asymptotic density of the poles of the eisenstein series for r a cofinite non cocompact subgroup of psl 2 r the question is known to be equivalent to the asymptotic count of the number of eigenvalues for the laplacebeltrami operator d acting in l2 h r where h is the upper halfplane with hyperbolic metric in general the spectral decomposition of d consists of the continuous band 1 4 oo with multiplicity the number of cusps of h r and a discrete component possibly in 1 4 0o spanned by eigenfunctions w1i wp2 see hj1 kb lxp for the eigenvalues aj dpj ajpj o consider the spectral counting function n r ij v n 0 see dips ps2 cor 2 3 luo lu recently established the unconditional result his argument does not involve the lindel6f hypothesis deshouillers et

nonstandard lorentz space forms in their recent paper 8 kulharni and raymond show that a closed 3 manifold which admits a complete lorentz metric of constant curvature 1 henceforth called a complete lorentz structure must be seifert fibered over a hyperbolic base furthermore on every such seifert fibered 3 manifold with nonzero euler class they construct such a lorentz metric moreover the lorentz structure they construct has a rather strong additional property which they call standard a lorentz structure is standard if its causal double cover possesses a timelike killing vector field equivalently it possesses a riemannian metric locally isometric to a left invariant metric on sl 2 r kulkarni and raymond asked if every closed 3 dimensional lorentz structure is standard this paper provides a negative answer to this question theorem 1 and a positive answer to the implicit question raised in 8 7 1 1 theorem 3 theorem 1 let m3 be a closed 3 manifold which admits a homogeneous lorentz structure and satisfies h m r 0 then there exists a nonstandard complete lorentz structure on m in 8 it is shown that the unit tangent bundle of a closed surface admits a homogeneous lorentz structure therefore we obtain corollary 2 there exists a complete lorentz structure on the unit tangent bundle of any closed surface f of genus greater than one which is not standard the homogeneous lorentz structures are all classified in 8 a circle bundle of euler number j over a closed surface f f 0 has a homogeneous structure if and only if j f an analogous statement holds when m has singular fibers i e when f is an orbifold we also show theorem 3 let m3 be a 3 manifold which admits a complete lorentz structure then m3 is not covered by a product f x s fa closed surface theorem 3 implies that the euler class of the seifert fiber structure of m3 is nonzero

actions propres sur les espaces homogenes reductifs let g be a linear semisimple real lie group and h be a re ductive subgroup of g we give a necessary and sufficient condition for the existence of a nonabelian free discrete subgroup r of g acting properly on g h for instance such a group r does exist for sl 2n ir sl 2n 1 ir but does not for sl 2n 1 r sl 2n r with n 1

proper action on a homogeneous space of reductive type an action of l on a homogeneous space g h is investigated where l h g are reductive lie groups a criterion of the properness of this action is obtained in terms of the little weyl group of g in particular r rankg r rankh iff calabi markus phenomenon occurs i e only finite subgroups of g can act properly discontinuously on g h then by using cohomological dimension theory of a discrete group l g h is proved compact iff d g d l d h where d g denotes the dimension of a riemannian symmetric space associated with g etc these results apply to the existence problem of lattice in g h several series of classical pseudo riemannian homogeneous spaces are found to admit non uniform lattice as well as uniform lattice while some necessary condition for the existence of uniform lattice is obtained when rankg rankh partially supported by grant in aid for scientific research no 63740074

whitney continua of curves in this paper we prove several theorems relating shape properties of whitney continua of curves in particular we investigate the fundamental dimension and the shape type of whitney continua of curves

shape properties of whitney maps for hyperspaces in this paper some shape properties of whitney maps for hyperspaces are investigated in particular the following are proved 1 let x be a continuum and let k be the hyperspace 2x or c x of x with the hausdorff metric then if x is any whitney map for for any 0 s s t w x t is an approximate strong deformation retract of w s t in particular sh w 1 t sh w 1 s t 2 pointed 1 movability is a whitney property 3 for any given n oo the property of cohomological dimension n is a sequential strong whitney reversible property 4 the property of being chainable or circle like is a sequential strong whitneyreversible property 5 the property of being an far is a whitney property for 1 dimensional continua property 2 is an affirmative answer to a problem of j t rogers 16 112 properties 3 and 4 are affirmative answers to problems of s b nadler 20 14 57 and 21 0 introduction by a continuum we mean a compact connected metric space for a given continuum x by the hyperspaces of x we mean 2x a c x i a is a nonempty closed subset of x c x a e 2x i a is connected which have the hausdorff metric pg see 20 the term mapping is a continuous function let a 2xor c x a mapping w 0 o x is called a whitney map for t 20 or 31 provided that the following conditions are satisfied a if a c b and a b then w a w b b o x 0 for each x e x in 1932 h whitney 31 showed that whitney maps always exist the notion of whitney map is a convenient and important tool for hyperspace theory a topological property p is said to be a whitney property 20 or 21 provided that whenever a continuum x has property p so does w f t for each whitney map w for c x and 0 t o x it is well known that connectibility is a whitney property if x is a received by the editors april 9 1985 and in revised form october 16 1985 1980 mathematics subject classification primary 54b20 secondary 54c55 54c56 54f45 kev words anid phrases hyperspaces whitney maps whitney property sequential strong whitneyreversible property approximate strong deformation retract pointed 1 movable far anr chainable circle like e mapping indecomposable 1986 american mathematical society 0002 9947 86 1 00 25 per page

whitney levels in hyperspaces of certain peano continua let x be a peano continuum let 2x resp c x be the space of all nonempty compacta resp subcontinua of x with the hausdorff matric let xo be a whitney map defined on sc 2x or c x such that x is admissible this requires the existence of a certain type of deformation of sc if sc c x assume x contains no free arc then for any to c 0 o x it is proved that w to o to and wf to o x are hilbert cubes this is an analogue of the curtis schori theorem for k a general result for the existance of admissible whitney maps is proved which implies that these maps exist when x is starshaped in a banach space or when x is a dendrite using these results it is shown for example that being an ar an anr an lc space or an lc space is not strongly whitney reversible introduction a continuum is a nonempty compact connected metric space a peano continuum is a locally connected continuum the hyperspaces of a continuum x are the spaces 2x a c x a is nonempty and compact and c x a c 2x a is connected metrized with the hausdorff metric 21 let f1 x x x c x a whitney map for a hyperspace sc of x is a continuous function w sc 0 xo such that o x 0 for each x c f1 x and if a b c c and a c b a then a b intuitively a whitney map is a size function if w is a whitney map for sc and 0 t o x then w l t is called a whitney level if 0 t x then w l t is called a positive whitney level thus a whitney level consists of compacta or continua in x of the same size basic facts about whitney maps and whitney levels are in 21 we note that whitney levels are coverings of x which as t gets close to zero converge to l 0 and consist of compacta of small diameter note that l 0 f1 x and hence l 0 is homeomorphic to x thus as t gets close to zero the whitney levels approximate x it is of interest to obtain information about the structure of positive whitney levels and to determine those properties which are preserved by the convergence of positive whitney levels to the zero level resultsa about this could be used to determine properties of x this is in analogy with the use of nerves of covers the nerves correspond to polyhedra these polyhedra approximate the original space as the mesh of the covers approaches zero and properties of these polyhedra determine various properties of the original space

deformation of proper actions on reductive homogeneous spaces let g be a real reductive lie group and h a closed reductive subgroup of g we investigate the deformation of standard compact quotients of g h that is of quotients of g h by discrete groups that are uniform lattices in some closed reductive subgroup l of g acting properly and cocompactly on g h for l of real rank 1 we prove that after a small deformation in g such a group keeps acting properly discontinuously and cocompactly on g h more generally we prove that the properness of the action of any convex cocompact subgroup of l on g h is preserved under small deformations and we extend this result to reductive homogeneous spaces g h over any local field as an application we obtain compact quotients of so 2n 2 u n 1 by zariski dense discrete subgroups of so 2n 2 acting properly discontinuously

deformation spaces associated to compact hyperbolic manifolds in this paper we take a first step toward understanding representations of cocompact lattices in so n 1 into arbitrary lie groups by studying the deformations of rational representations see proposition 5 1 for a rather general existence result this proposition has a number of algebraic applications for example we remark that such deformations show that the margulis super rigidity theorem see 30 cannot be extended to the rank 1 case we remark also that if so n 1 is one of the standard arithmetic examples described in section 7 then has a faithful representation in so n 1 the galois conjugate of the uniformization representation and proposition 5 1 may be used to deform the direct sum of and the trivial representation in so n 2 thereby constructing non trivial families of irreducible orthogonal representations of however most of this paper is devoted to studying certain spaces of representations which are of interest in differential geometry in a sense which we now explain

finite parts of the spectrum of a riemann surface let s and s be compact riemann surfaces of the same genus g g ge 2 endowed with the poincare metric of constant negative curvature 1 par the authors show that for every epsilon 0 there exists an integer m m g epsilon with the property assume that 1 injectivity radius of s and s ge epsilon and 2 the first m m g epsilon eigenvalues of the laplacian of s and s coincide then s and s are isospectral par the authors conjecture that the integer m will not depend on epsilon that is the theorem holds with an integer which depends only on the genus par for the proof a model of teichmuller space is described and the analyticity of the resolvent of laplacian on this space is proved also the authors note that the injectivity radius is estimated by a finite part of the spectrum the number of eigenvalues of the laplacian in the interval 1 4 1

dimension of binary convex structures it is shown that for compact spaces with a normal binary convexity the dimension functions dim ind ind and cohomological dimension are all equal also an h dimensional compact space x with a normal binary convexity embeds in a product of an m dimensional connected quotient of x with the space of xcomponents both results are obtained with the aid of an auxiliary theory of convex dimension some applications to completely distributive lattices are given 0 introduction for a connected and completely distributive lattice it is known 2 3 4 that the lebesgue covering dimension dim and the cohomological dimension cdg where g is an abelian coefficient group are equal by 3 corollary 1 the small inductive dimension ind equals cdg provided that in addition the set of points at which the lattice attains its small inductive dimension has non void interior we have taken up the equality problem for the various dimension functions at the following general level let x be a normal binary that is with helly number at most 2 convex structure with compact polytopes according to 32 all intervals of x are completely distributive lattices under suitably chosen base point orders on the other hand the space x with its weak topology embeds as a median stable subset of a tychonov cube our first main result is as follows 0 1 theorem x is a compact space with a normal binary convexity then for each coefficient group g cdgx dim x ind x ind x if instead of being compact x is only required to have compact polytopes and if a is lindelof in its weak topology then it is still true that dimx indx in 34 a result similar to theorem 0 1 has been obtained for a restricted class of lawson semilattices also there is a theorem of pasynkov 23 p 722 of the english translation asserting that dim ind ind for locally compact groups one is tempted to conclude that dimension functions tend to coincide on topological algebras see 32 3 6 for the algebraicity of binary convexities the equality theorem 0 1 actually involves one other dimension function the socalled convex dimension cind this function defined on topological convex structures only was studied in 28 for convex structures with connected convex sets and it will be the key tool in proving theorem 0 1 for convexities with connected convex sets but with an unrestricted helly number an equality theorem of the above type has already been obtained in 22 where cohomological dimension was not considered to eliminate the connectedness restriction we have re examined cind in the case of non connected convex sets and it appears that the main results of 28 survive for proc london math soc 3 48 1984 34 54 dimension of binary convex structures 35 binary convex structures this almost self contained treatment of cind is given in 1 a proof of theorem 0 1 is given in 2 together with some consequences for instance we use results of 29 concerning convexity invariants to re prove the well known equality of breadth and dimension for connected completely distributive lattices see 2 corollary 3 4 3 corollary 1 17 corollary 2 4 our second main result is the following 0 2 theorem let x be an n dimensional compact space with a normal binary convexity then there exists a convexity preserving quotient q x qx onto an n dimensional connected space qx with a normal binary convexity such that q together with the decomposition map d x dx the space of components gives an embedding of topological convex structures

optimal information acquisition for a linear quadratic control problem this paper develops a generalization of the linear quadratic control problem with partial information as in the standard partial information setting it is assumed that the state variable is only observed with noise the idea in this paper is that the information level may be chosen optimally in real life information is costly to acquire it is therefore a trade off between the costs of getting detailed information and the increased value this information gives we believe that the technique we present should have potential for application within both economics and engineering

analysis on the minimal representation of o p q abstract for the group o p q we give a new construction of its minimal unitary representation via euclidean fourier analysis this is an extension of the q 2 case where the representation is the mass zero spin zero representation realized in a hilbert space of solutions to the wave equation the group o p q acts as the mobius group of conformal transformations on r p 1 q 1 and preserves a space of solutions of the ultrahyperbolic laplace equation on r p 1 q 1 we construct in an intrinsic and natural way a hilbert space of solutions so that o p q becomes a continuous irreducible unitary representation in this hilbert space we also prove that this representation is unitarily equivalent to the representation on l2 c where c is the conical subvariety of the nilradical of a maximal parabolic subalgebra obtained by intersecting with the minimal nilpotent orbit in the lie algebra of o p q

kakutani property of the polytopes implies kakutani property of the whole space abstract this paper deals with the following property of a space x for every upper semicontinuous function from x to nonempty closed convex subsets of x there exists x 0 which is in x 0 we derive this property of x from the same property assumed to hold for the polytopes in x convexity in our setup is given in an abstract axiomatic way the results are also reformulated in the order theoretical language of continuous lattices our results directly generalize a an extension of the kakutani fixed point theorem to compact convex sets in locally convex spaces due to ky fan and i l glicksberg and b the fixed point theorem of wallace concerning set valued functions on trees

do markets favor agents able to make accurate predictions blume and easley 1992 show that if agents have the same savings rule those who maximize the expected logarithm of next period s outcomes will eventually hold all wealth i e are most prosperous however if no agent adopts this rule then the most prosperous are not necessarily those who make the most accurate predictions thus agents who make inaccurate predictions need not be driven out of the market in this paper it is shown that among agents who have the same intertemporal discount factor and who choose savings endogenously the most prosperous are those who make accurate predictions hence convergence to rational expectations obtains because agents who make inaccurate predictions ar1e driven out of the market

geometric realization of discrete series for semisimple symmetric spaces let g be a connected semisimple lie group a an involution of g and h the connected component of the fixed point set of a containing the identity then g h is a semisimple symmetric space we assume g is a real form of a complex lie group and rank g h rank k k c h where k is a a stable maximal compact subgroup of g flensted jensen using his duality principle and poisson transform constructed countably many discrete series in u g h f j i then using deep results of hyperfunction theory and microlocal analysis oshima and matsuki gave a detailed characterization of these discrete series including a proof of flensted jensen s conjecture c 0 om based on these results we give the discrete series a geometric interpretation in locally symmetric spaces f c where g k and f cg is a cocompact discrete group such that f c h c h is cocompact our geometric interpretation is the following first of all to a flensted jensen function which is the generating function of a discrete series v we associate a harmonic form cb z on g with values in a finite dimensional g module v right g translates of coefficients of 5z realizes the contragredient t of r and tba is left invariant under h and under right k action it transforms according to the minimal k type with highest weight of 3 is the pull back of a v valued from coz on and v determines a locally constant bundle e on f so that if convergence holds

wave front sets of reductive lie group representations iii abstract let g be a real reductive algebraic group and let x be a homogeneous space for g with a non zero invariant density we give an explicit description of a zariski open dense subset of the asymptotics of the tempered support of l 2 x under additional hypotheses this result remains true for vector bundle valued harmonic analysis on x these results follow from an upper bound on the wave front set of an induced lie group representation under a uniformity condition

the plancherel decomposition for a reductive symmetric space i spherical functions we prove the plancherel formula for spherical schwartz functions on a reductive symmetric space our starting point is an inversion formula for spherical smooth compactly supported functions the latter formula was earlier obtained from the most continuous part of the plancherel formula by means of a residue calculus in the course of the present paper we also obtain new proofs of the uniform tempered estimates for normalized eisenstein integrals and of the maass selberg relations satisfied by the associated c functions

discrete groups and non riemannian homogeneous spaces a basic question in geometry is to understand compact locally homogeneous manifolds i e those compact manifolds that can be locally modelled on a homogeneous space j h of a finite dimensional lie group h this means that there is an atlas on a manifold m consisting of local diffeomorphisms with open sets in j h where the transition functions between these open sets are given by translations by elements of h a basic example is the case of m j h f where f c h is a discrete subgroup acting freely and properly discontinuously on j h with a compact quotient these examples can be abstractly characterized as the complete case see g we then call f a cocompact lattice on j h when j is compact j h has an h invariant riemannian metric so that m itself becomes a riemannian manifold in a natural way thus the class of locally homogeneous riemannian manifolds includes but is not exhausted by the locally symmetric spaces for h aff rn and j gl n r the spaces j h f are the complete affinely flat manifolds a non riemannian example which has been extensively studied when h is simple and j is not compact the situation is far from being well understood some special series of such homogeneous spaces admitting a cocompact lattice have been constructed by kulkarni ku and by t kobayashi k for example kulkarni shows the existence of such a discrete group f for the homogeneous spaces so 1 2n so 2 2n and kobayshi does the same for u 1 n so 2 2n on the other hand the constructions they give for these and other similar series are quite special and there has been the general suspicion that most homogeneous spaces j h with h simple and j not compact do not admit a cocompact lattice we recall that when j is compact i e the riemannian case such f always exist by a result of borel b one general situation in which it is known that no such f exists is the case in which j h is noncompact and of reductive type and r rank h r rank j this situation was studied by calabi markus cm wolf w and kobayashi k and the nonexistence of f in this situation is a special case of a more general result known as the calabi markus phenomenon kobayashi and ono ko use the hirzebruch proportionality principle to show that some other special series do

deformation of compact clifford klein forms of indefinite riemannian homogeneous manifolds 1 1 let g be a lie group and h a closed subgroup of g if a discrete subgroup of g acts properly discontinuously and freely on g h then the double coset space g h carries naturally a manifold structure such that the quotient map g h g h is locally diffeomorphic the manifold g h is said to be a clifford klein form of g h if it is compact then is said to be a uniform lattice for g h a typical example is a compact riemann surface mg with genus g 2 which is biholomorphic to a compact clifford klein form of the poincare disk g h sl 2 r so 2 by the uniformization theorem it is important from geometric view point that a clifford klein form g h inherits any g invariant local geometric structure on g h such as indefinite riemannian metric complex structure symplectic structure causal structure and so on

on limit multiplicites of discrete series representations in spaces of automorphic forms of course the groups f are then arithmetic subgroups of g in this situation it seems natural to assume that as n the spectral decomposition of l2 f g will approximate that of g in particular let 3 be a discrete series representation of g if f is a subgroup of g let re f 6 be the multiplicity of 3 in the representation of g by right translations on l2 f g choose a haar measure dg on g if f is arithmetic let v f g be the finite volume of f g for the measure induced by dg let d 3 be the formal degree of 3 for the measure dg

classification of semisimple symmetric spaces with proper actions we give a complete classification of irreducible symmetric spaces for which there exist proper sl 2 mathbb r actions as isometries using the criterion for proper actions by t kobayashi and combinatorial techniques of nilpotent orbits in particular we classify irreducible symmetric spaces that admit surface groups as discontinuous groups combining this with benoist s theorem

nash points ky fan inequality and equilibria of abstract economies in max plus and b convexity abstract b convexity was introduced in w briec c horvath b convexity optimization 53 2004 103 127 separation and hahn banach like theorems can be found in g adilov a m rubinov b convex sets and functions numer funct anal optim 27 2006 237 257 and w briec c d horvath a rubinov separation in b convexity pacific j optim 1 2005 13 30 we show here that all the basic results related to fixed point theorems are available in b convexity ky fan inequality existence of nash equilibria and existence of equilibria for abstract economies are established in the framework of b convexity monotone analysis or analysis on maslov semimodules v n kolokoltsov v p maslov idempotent analysis and its applications math appl vol 401 kluwer academic 1997 v p litvinov v p maslov g b shpitz idempotent functional analysis an algebraic approach math notes 69 2001 696 729 v p maslov s n samborski eds idempotent analysis advances in soviet mathematics amer math soc providence ri 1992 is the natural framework for these results from this point of view max plus convexity and b convexity are isomorphic maslov semimodules structures over isomorphic semirings therefore all the results of this paper hold in the context of max plus convexity

some properties of abstract convexity structures on topological spaces abstract in this paper we establish some relationships among abstract convexity the selection property and the fixed point property we show that if a convexity structure c defined on a topological space has the selection property then c satisfies the h condition moreover in an l c compact metric space the selection property implies the fixed point property

set relations and set systems induced by some families of integral domains abstract in this paper given an integral domain u we investigate the main properties of a relation m o d which is based on the interrelation between subdomains of u and finitely generated unitary submodules of u we shall characterize it in terms of a second relation between n tuples u 1 u n of elements of u and subdomains d of u defined by the vanishing in u 1 u n of some polynomial p z 1 z n belonging to a specific subset of the polynomial ring in several variables d z 1 z n such an equivalence shall be used in order to introduce three specific collections of subdomains x u b u and p u whose algebraic properties present a close connection with geometrical and combinatorial properties induced by m o d on the other hand the characterization of the subdomains of x u leads to the more general problem of finding a map associating with a subdomain d of u a collection d of subdomains of k u such that the intersection of some or of any member of d gives d in this perspective in the present paper we shall study two further collections of subdomains of u denoted respectively by e u and l u whose main properties are related to those of the families p u and b u finally our investigation of all the aforementioned subdomain families shall be also related to the study of pairs e where e u 0 and is an idempotent ring endomorphism of u whose kernel agrees with the ideal of u generated by e we shall exhibit several results concerning the membership of u and of u e to the above subdomain families

anosov representations domains of discontinuity and applications the notion of anosov representations has been introduced by labourie in his study of the hitchin component for sl n r subsequently anosov representations have been studied mainly for surface groups in particular in the context of higher teichmuller spaces and for lattices in so 1 n in this article we extend the notion of anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties in particular given an anosov representation g we explicitly construct open subsets of compact g spaces on which acts properly discontinuously and with compact quotient as a consequence we show that higher teichmuller spaces parametrize locally homogeneous geometric structures on compact manifolds we also obtain applications regarding non standard compact clifford klein forms and compactifications of locally symmetric spaces of infinite volume

the law of large demand for information an unresolved problem in bayesian decision theory is how to value and price information this paper resolves both problems assuming inexpensive information building on large deviation theory we produce a generically complete asymptotic order on samples of i i d signals in finite state finite action models computing the marginal value of an additional signal we find it is eventually exponentially falling in quantity and higher for lower quality signals we provide a precise formula for the information demand valid at low prices asymptotically a constant times the log price and falling in the signal quality for a given price

discrete decomposability of the restriction of a q λ with respect to reductive subgroups and its applications letg g be real reductive lie groups and q a stable parabolic subalgebra of lie g this paper offers a sufficient condition on g g q that the irreducible unitary representation mathop a q limits ofg with non zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroupg each of finite multiplicity as an application to purely analytic problems new results on discrete series are also obtained for some pseudo riemannian non symmetric spherical homogeneous spaces which fit nicely into this framework some explicit examples of a decomposition formula are also found in the cases wherea q is not necessarily a highest weight module

analysis on the minimal representation of o p q ii branching laws this is a second paper in a series devoted to the minimal unitary representation of o p q by explicit methods from conformal geometry of pseudo riemannian manifolds we find the branching law corresponding to restricting the minimal unitary representation to natural symmetric subgroups in the case of purely discrete spectrum we obtain the full spectrum and give an explicit parseval plancherel formula and in the general case we construct an infinite discrete spectrum r 2003 published by elsevier science usa msc 22e45 22e46 53a30 43a85

a selection theorem for topological convex structures a continuous selection theorem has been obtained for multivalued functions the values of which are convex sets of certain synthetic convex structures applications are given related with superextensions semi lattices spaces of order arcs trees whitney levels in hyperspaces and geometric topology applications to traditional convexity in vector spaces involve beer s approximation theorem and a fixed point theorem of dugundji granas some other applications a o an invariant arc theorem appear elsewhere

eigenspaces of the laplacian on hyperbolic spaces composition series and integral transforms abstract let x be a projective real complex or quaternion hyperbolic space realized as the pseudo riemannian symmetric space x g h with g o p q u p q or sp p q these are the classical isotropic symmetric spaces let be the g invariant laplace beltrami operator on x a complete description by k types for each c of all closed g invariant subspaces of the eigenspace f c x f f is given the eigenspace representations are compared with principal series representations using poisson transformations similar results are obtained also for the exceptional isotropic symmetric space the langlands parameters of the spherical discrete series representations are determined