the cusped hyperbolic orbifolds of minimal volume in dimensions less than ten abstract we detect the cusped complete hyperbolic orbifolds of minimal volume in dimensions less than ten our method is geometric and uses results from crystallography and the theory of sphere packings in fact such an n orbifold gives rise to a horoball packing whose orthogonal projection to the cusp boundary yields the densest euclidean lattice packing in dimension n 1

the densest lattices in pgl3 q2 abstract we find the smallest possible covolume for lattices in pgl 3 q 2 show that there are exactly two lattices with this covolume and describe them explicitly they are commensurable and one of them appeared in mumford s construction of his fake projective plane we also discuss a new 2 adic uniformization of another fake projective plane

on character varieties sets of discrete characters and nonzero degree maps a it knot manifold is a compact connected irreducible orientable 3 manifold whose boundary is an incompressible torus we first investigate virtual epimorphisms between the fundamental groups of small knot manifolds and prove minimality results for small knot manifolds with respect to nonzero degree maps these results are applied later in the paper where we fix a small knot manifold m and investigate various sets of characters of representations rho pi 1 m to rm psl 2 bbb c whose images are discrete we show that the topology of these sets is intimately related to the algebraic structure of the rm psl 2 bbb c character variety of m as well as dominations of manifolds by m and its dehn fillings we apply our results to the following question of shicheng wang it are nonzero degree maps between infinitely many distinct dehn fillings of two hyperbolic knot manifolds m and n induced by a nonzero degree map m to n we show that the answer is yes generically using this we show that if a small mathcal h minimal hyperbolic knot manifold admits non homeomorphic mathcal h minimal dehn fillings it admits infinitely many such fillings we also construct the first infinite families of small closed connected orientable manifolds which are minimal in the sense that they do not admit nonzero degree maps other than homotopy equivalences to any aspherical manifold

streamline topologies near a stationary wall of stokes flow in a cavity two dimensional stokes flow in a rectangular single lid driven cavity with the upper lid moving is considered to investigate streamline topologies near a stationary wall by using both of the qualitative theory and an analytic solution we consider the velocity field by expanding in a taylor series at the origin a systematic use of normal form transformations results in a much simplified system of differential equations for the streamlines encapsulating all features of the original system using the simplified system a sequence of possible bifurcations of streamlines is obtained close to a simple linear degeneracy then to extract the same streamline topologies by varying a physical parameter the cavity aspect ratio we used an eigenfunction solution for the streamfunction

polynomial sequences of bounded operators the basic results of spectral theory are obtained using the sequence of powers of a bounded linear operator t t2 tn in this paper we replace the powers tn by certain polynomials pn t and make use of special properties of the polynomial sequence pn n 0 to derive some new results concerning operators for example using an arbitrary polynomial sequence pn n 0 we obtain binomial spectral radii and semidistances which reduce in the case of the sequence of powers to the usual spectral radius and semidistance

lattices of minimum covolume in chevalley groups over local fields of positive characteristic in this article we show that if g is a simply connected chevalley group of either classical type of rank bigger than 1 or type e6 and q 9 is a power of a prime number p 5 then g g fq t 1 up to an automorphism has a unique lattice of minimum covolume which is g fq t 1

topological flow structures in an l shaped cavity with horizontal motion of the upper lid the flow patterns in a steady viscous l shaped cavity are investigated using both analytic solutions combined with methods from nonlinear dynamical systems and numerically using the finite element method a boundary value problem is formulated for the case of stokes flow which is solved analytically j expressed as an infinite series of eigenfunctions which depend on h 1 and h 2 which are related to the heights of the l shaped domain the h 1 h 2 control space diagram is constructed for exhibiting the mechanism by which new eddies are obtained in the cavity

arithmeticity discreteness and volume we give an arithmetic criterion which is sufficient to imply the discreteness of various two generator subgroups of p sl 2 c we then examine certain two generator groups which arise as extremals in various geometric problems in the theory of kleinian groups in particular those encountered in efforts to determine the smallest co volume the margulis constant and the minimal distance between elliptic axes we establish the discreteness and arithmeticity of a number of these extremal groups the associated minimal volume arithmetic group in the commensurability class and we study whether or not the axis of a generator is simple

geometric representation theory for unitary groups of operator algebras geometric realizations for the restrictions of gns representations to unitary groups of c algebras are constructed these geometric realizations use an appropriate concept of reproducing kernels on vector bundles to build such realizations in spaces of holomorphic sections a class of complex coadjoint orbits of the corresponding real banach lie groups are described and some homogeneous holomorphic hermitian vector bundles that are naturally associated with the coadjoint orbits are constructed

a lower bound for the volume of hyperbolic 3 orbifolds toutes les 3 varietes d orbites orientables completes ont un volume au moins 0 0000013 toutes les 3 varietes d orbites hyperboliques orientables completes cuspides ont un volume au moins 3 1 2 24

spectra for solvable lie algebras of bundle endomorphisms the aim of the paper is to investigate spectral properties of the lie algebras corresponding to the symmetry groups of certain flags of vector bundles over a compact space under natural hypotheses such lie algebras are solvable being in general infinite dimensional the spectral theory of finite dimensional solvable lie algebras of operators is extended to this natural class of infinite dimensional solvable lie algebras the discussion uses the language of continuous fields of c algebras the flag manifolds in c algebraic framework are naturally involved here they providing the basic method for obtaining flags of vector bundles

covolumes of nonuniform lattices in pu n 1 this paper studies the covolumes of nonuniform arithmetic lattices in pu n 1 we determine the smallest covolume nonuniform arithmetic lattices for each n the number of minimal covolume lattices for each n and study the growth of the minimal covolume as n varies in particular there is a unique lattice up to isomorphism in pu 9 1 of smallest euler poincare characteristic amongst all nonuniform arithmetic lattices in pu n 1 we also show that for each even n there are arbitrarily large families of nonisomorphic maximal nonuniform lattices in pu n 1 of equal covolume

saddle connections near degenerate critical points in stokes flow within cavities streamline patterns and their bifurcations in two dimensional incompressible flow near a simple degenerate critical point away from boundaries are investigated by using the normal form theory for the streamfunction obtained by m brons j n hartnack streamline topologies near simple degenerate critical points in two dimensional flow away from boundaries phys fluids 11 1999 314 324 for the normal form of order six a bifurcation diagram is constructed with two bifurcation parameters the theory is applied to the patterns and bifurcations found numerically in the studies of stokes flow in a double lid driven rectangular cavity with two control parameters the cavity aspect ratio a height to width and the speed ratio s bifurcations in the cavity are obtained using an analytic solution for the streamfunction developed for any value of s and a using this solution for special values s a a global bifurcation is identified with a single heteroclinic connection which connects three saddle points in a triangle and does not appear in the unfolding of the simple linear degenerate critical points lying in a line y constant

irreducible representations of infinite dimensional lie algebras abstract some results concerning the operatorially irreducible topologically irreducible operatorially and topologically irreducible representations of a class of infinite dimensional lie algebras by bounded operators in a complex banach space are obtained

spiraling spectra of geodesic lines in negatively curved manifolds given a negatively curved geodesic metric space m we study the asymptotic penetration behaviour of geodesic lines of m in small neighbourhoods of closed geodesics and of other compact convex subsets of m we define a spiraling spectrum which gives precise information on the asymptotic spiraling lengths of geodesic lines around these objects we prove analogs of the theorems of dirichlet hall and cusick in this context as a consequence we obtain diophantine approximation results of elements of mathbb r mathbb c or the heisenberg group by quadratic irrational ones