the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

balanced metrics on non kahler calabi yau threefolds we construct balanced metrics on the family of non kahler calabi yau threefolds that are obtained by smoothing after contracting 1 1 rational curves on a kahler calabi yau threefold as an application we construct balanced metrics on complex manifolds diffeomorphic to the connected sum of k ge 2 copies of s 3 s 3

the fu yau equation with negative slope parameter the fu yau equation is an equation introduced by fu and yau as a generalization to arbitrary dimensions of an ansatz for the strominger system as in the strominger system it depends on a slope parameter alpha prime the equation was solved in dimension 2 by fu and yau in two successive papers for alpha prime 0 and for alpha prime 0 in the present paper we solve the fu yau equation in arbitrary dimension for alpha prime 0 to our knowledge these are the first non trivial solutions of the fu yau equation in any dimension strictly greater than 2

properties of manifolds with skew symmetric torsion and special holonomy abstract in this paper we provide examples of hypercomplex manifolds which do not carry hkt structures thus answering a question in grantcharov and poon comm math phys 213 2000 19 we also prove that the existence of an hkt structure is not stable under small deformations similarly we provide examples of compact complex manifolds with vanishing first chern class which do not admit a hermitian structure whose bismut connection has restricted holonomy in su n thus providing a counter example to the conjecture in gutowski et al deformations of generalized calibrations and compact non kahler manifolds with vanishing first chern class math dg 0205012 asian j math to appear again we prove that such a property is not stable under small deformations

a minmax regret approach to the critical path method with task interval times abstract the execution of a given project with a number of interrelated tasks due to precedence constraints represents a challenge when one must to control the available resources and the compromised due dates in this paper we analyse this problem under uncertain individual task completing times specifically we will assume that a given range for the admissible values of each individual completing time is available taking into account that the precedence relations between tasks must be preserved each realization of the admissible execution times for the set of tasks will define a new scenario determining the ending time for the project and the subset of critical tasks the minmax regret criterion will be used in order to obtain a robust approximation to the critical set of tasks determining the overall execution time for the project

characterizing volume via cone duality for divisors over smooth projective varieties we show that the volume can be characterized by the duality between the pseudo effective cone of divisors and the movable cone of curves inspired by this result we define and study a natural intersection theoretic volume functional for 1 cycles over compact kahler manifolds in particular for numerical equivalence classes of curves over projective varieties it is closely related to the mobility functional studied by lehmann

fuzzy shortest path problems incorporating interactivity among paths abstract this paper deals with a shortest path problem on a network in which a fuzzy number instead of a real number is assigned to each arc length such a problem is ill posed because each arc cannot be identified as being either on the shortest path or not therefore based on the possibility theory we introduce the concept of degree of possibility that an arc is on the shortest path every pair of distinct paths from the source node to any other node is implicitly assumed to be noninteractive in the conventional approaches this assumption is unrealistic and involve inconsistencies to overcome this drawback we define a new comparison index between the sum of fuzzy numbers by considering interactivity among fuzzy numbers an algorithm is presented to determine the degree of possibility for each arc on a network finally this algorithm is evaluated by means of large scale numerical examples consequently we can find this approach is efficient even for real world practical networks

stochastic and fuzzy pert the key issue in project planning under uncertainty is the choice of a time schedule for further action such a time schedule which is necessary for the subcontractors because they often have to order materials and labour in advance will not automatically be generated by the analysis of the randomness and the imprecision in the project it is the result of a decision the obvious importance of the time schedule will extensively be dicussed in the sections to follow we present a fuzzy version of the project evaluation and review technique pert which is computationally easier to use than the original probabilistic version the fuzzy version also avoids several shortcomings of the probabilistic version

computing latest starting times of activities in interval valued networks with minimal time lags abstract this paper deals with problems of determining possible values of earliest and latest starting times of an activity in networks with minimal time lags and imprecise durations that are represented by means of interval or fuzzy numbers although minimal time lags are practical in different projects former researchers have not considered these problems after proposing propositions which reduce the search space a novel polynomial algorithm is presented to compute intervals of possible values of latest starting times in interval valued networks with minimal time lags then the results are extended to networks with fuzzy durations

the computational complexity of the criticality problems in a network with interval activity times abstract the paper analyzes the criticality in a network with interval activities duration times a natural generalization of the criticality notion for a path an activity and an event for the case of network with interval activity duration times is given the computation complexity of five problems linked to the introduced criticality notion is presented

on computing the latest starting times and floats of activities in a network with imprecise durations the paper deals with the problems of computing the intervals of possible values of the latest starting times and floats of activities in networks with imprecise durations represented by means of interval or fuzzy numbers so far these problems have been completely solved when the networks are series parallel we propose new polynomial algorithms for determining the intervals of the latest starting times in general networks we also present some complexity results for floats the computation of floats is probably intractable and describe some polynomially solvable cases then we extend the results to networks with fuzzy durations

on combinatorial optimization problems on matroids with uncertain weights in this paper the combinatorial optimization problem on weighted matroid is considered it is assumed that the weights in the problem are ill known and they are modeled as fuzzy intervals the optimality of solutions and the optimality of elements are characterized this characterization is performed in the setting of possibility theory a method of choosing a solution under uncertainty is also proposed

generators of large subgroups of units of integral group rings of nilpotent groups let g be a finite nilpotent group so that all simple components d n n n 2 of qg satisfy the congruence subgroup theorem suppose that for all odd primes p dividing g the hamiltonian quaternions h split over the pth cyclotomic field q p then new units b3 are introduced so that b1 b2 b 2 b3 is of finite index in u zg

geometry of compact complex homogeneous spaces with vanishing first chern class abstract we prove that any compact complex homogeneous space with vanishing first chern class after an appropriate deformation of the complex structure admits a homogeneous calabi yau with torsion structure provided that it also has an invariant volume form a description of such spaces among the homogeneous c spaces is given as well as many examples and a classification in the 3 dimensional case we calculate the cohomology ring of some of the examples and show that in dimension 14 there are infinitely many simply connected spaces admitting such a structure with the same hodge numbers and torsional chern classes we provide also an example solving the strominger s equations in heterotic string theory

on the upper estimate of the heat kernel of a complete riemannian manifold let m be a complete non compact riemannian manifold whose sectional curvature is bounded between two constants k and k then one expects that the heat diffusion in such a manifold behaves like the heat diffusion in euclidean space the purpose of this paper is to give a justification of such a statement in 5 j cheeger and the third author found a lower estimate of the heat kernel by comparing it with the heat kernel of the space form whose curvature is the lower bound of the curvature of the manifold this lower estimate is sharp if we insist the dependence should be on the lower bound of the ricci curvature alone it remains to give an upper estimate of the heat kernel one does not however expect to have a comparison theorem for the upper bound because it is more sensitive to the geometry of the manifold in fact the heat kernel of the upper hialf space and the heat kernel of the complete hyperbolic manifold with finite volume have quite different behavior this is reflected by the fact that the laplacian has no discrete spectrum in the first case while infinite number of discrete eigenvalues may exist in the latter case what we will prove here is that in any case the heat kernel has to decay in a manner similar to the euclidean heat kernel thus we will prove that for any constant c 4 there exists c1 depending on c t the bound of the curvature of m and x so that for all t e 0 t

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

critical path analysis in the network with fuzzy activity times a natural generalization of the criticality notion in a network with fuzzy activity times is given it consists in direct application of the extension principle of zadeh to the notion of criticality of a path an activity an event treated as a function of the activities duration times in the network there are shown some relations between the notion of fuzzy criticality introduced in the paper and the notion of interval criticality criticality in the network with interval activity times proposed by the authors in another paper two methods of calculation of the path degree of criticality according to the proposed concept of fuzzy criticality are presented

equations du type de monge ampere sur les varietes hermitiennes compactes resume soit x g une variete hermitienne compacte si c 2 x soit m det etude d equations de la forme m f x ou f c tx r est une fonction partout strictement positive ayant une croissance exponentielle en et majoree par une puissance de la norme du gradient de let x g be a hermitian compact manifold for c 2 x let m det study of equations of the form m f x where f c tx r is an everywhere strictly positive function with an exponential growth in and which is bounded by a power of the norm of the gradient of

on a class of fully nonlinear elliptic equations on closed hermitian manifolds ii l estimate we study a class of fully nonlinear elliptic equations on closed hermitian manifolds under the assumption of the cone condition we derive the l estimate directly as an application we solve the complex quotient equations on closed kahler manifolds 2016 wiley periodicals inc

the fu yau equation on compact astheno kahler manifolds abstract in this paper we study the fu yau equation on compact hermitian manifolds and prove the existence of solutions of equation on astheno kahler manifolds we also prove the uniqueness of solutions of fu yau equation when the slope parameter is negative

the personalization of security selection an application of fuzzy set theory abstract we apply the theory of fuzzy subsets to the multiple objective decision problem of stock selection we allow our objectives to have varying degrees of importance we discuss various criteria used in selecting stocks we indicate some procedures for subjectively evaluating the membership functions associated with these criteria

a flow of conformally balanced metrics with kahler fixed points while the anomaly flow was originally motivated by string theory its zero slope case is potentially of considerable interest in non kahler geometry as it is a flow of conformally balanced metrics whose stationary points are precisely kahler metrics we establish its convergence on kahler manifolds for suitable initial data we also discuss its relation to some current problems in complex geometry

a local index theorem for non kahler manifolds on considere des conditions suffisantes pour qu un theoreme d indice local soit vrai pour un operateur de dirac associe a une connexion qui ne coincide pas necessairement avec la connexion de levi civita l

fuzzy scheduling modelling flexible constraints vs coping with incomplete knowledge abstract an overview of some fuzzy set based approaches to scheduling is proposed emphasizing two distinct uses of fuzzy sets representing preference profiles and modelling uncertainty distributions the first setting leads to a valued non compensatory generalization of constraint directed scheduling the other setting yields a possibility theoretic counterpart of pert where probability distributions of activity durations are changed into possibility distributions for the purpose of modelling incomplete information it is pointed out that a special case of the latter interval valued pert is a difficult ill known problem regarding the determination of critical activities latest starting times and floats lastly when flexible constraints and uncertain processing times are to be jointly considered the use of possibilistic decision theory leads to the computation of robust schedules

viscosity solutions to complex hessian equations we study viscosity solutions to complex hessian equations in the local case we consider a bounded domain in cn the standard kahler form in cn and 1 m n under some suitable conditions on f g we prove that the equation ddc m n m f x n g on admits a unique viscosity solution modulo the existence of subsolution and supersolution if moreover the datum is holder continuous then so is the solution in the global case let x be a compact hermitian homogeneous manifold where is an invariant hermitian metric not necessarily kahler we prove that the equation ddc m n m f x n has a unique viscosity solution under some natural conditions on f

the dirichlet problem for a complex monge ampere type equation on hermitian manifolds abstract we are concerned with fully nonlinear elliptic equations on hermitian manifolds and search for technical tools to overcome difficulties in deriving a priori estimates which arise due to the nontrivial torsion and general non pseudoconvex boundary data we present our methods which work for more general equations by considering a specific equation which resembles the complex monge ampere equation in many ways but with crucial differences our work is motivated by recent increasing interests in fully nonlinear equations on complex manifolds from geometric problems

relations between the kahler cone and the balanced cone of a kahler manifold abstract in this paper we consider a natural map from the kahler cone of a compact kahler manifold to its balanced cone we study its injectivity and surjectivity we also give an analytic characterization theorem on a nef class being kahler

on the evolution of a hermitian metric by its chern ricci form we consider the evolution of a hermitian metric on a compact complex manifold by its chern ricci form this is an evolution equation first studied by m gill and coincides with the kahler ricci flow if the initial metric is kahler we find the maximal existence time for the flow in terms of the initial data we investigate the behavior of the flow on complex surfaces when the initial metric is gauduchon on complex manifolds with negative first chern class and on some hopf manifolds finally we discuss a new estimate for the complex monge ampere equation on hermitian manifolds

minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights this paper deals with a general combinatorial optimization problem in which closed intervals and fuzzy intervals model uncertain element weights the notion of a deviation interval is introduced which allows us to characterize the optimality and the robustness of solutions and elements the problem of computing deviation intervals is addressed and some new complexity results in this field are provided possibility theory is then applied to generalize a deviation interval and a solution concept to fuzzy ones

some methods for evaluating the optimality of elements in matroids with ill known weights in this paper a class of matroidal combinatorial optimization problems with imprecise weights of elements is considered the imprecise weights are modeled by intervals and fuzzy intervals the concepts of possible and necessary optimality under imprecision are recalled some efficient methods for evaluating the possible and necessary optimality of elements in the interval valued problems are proposed some efficient algorithms for computing the exact degrees of possible and necessary optimality of elements in the fuzzy valued problems are designed

a path enumeration approach for the analysis of critical activities in fuzzy networks this paper addresses the problem of determining the degree of possible and necessary criticality of activities as well as determining paths in networks that have fuzzy activity durations in such networks activities and paths are reported in a fuzzy representation as being critical with certain degrees of possibility and necessity instead of being declared critical or not in a binary way although the problem of computing the possibility and necessity degrees of criticality for paths have been investigated in the literature those problems for activities have not yet been addressed herein an efficient algorithm that relies on a path enumeration technique is proposed to compute the possibility degrees of criticality of activities additionally the proposed algorithm computes paths with maximum and minimum degrees for the necessity of criticality which correspond to activities real world project networks were used to evaluate the performance of the algorithm

a variational theory of the hessian equation by studying a negative gradient flow of certain hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous hessian equations to achieve this we derive uniform first and second order a priori estimates for the elliptic and parabolic hessian equations our results generalize well known results for semilinear elliptic equations and the monge ampere equation c 2001 john wiley sons inc

fully nonlinear elliptic equations for conformal deformations of chern ricci forms abstract we study a general class of fully nonlinear elliptic equations of second order on hermitian manifolds we derive a priori estimates and prove some existence results for these equations in particular we prove interior estimates for the complex hessian which in general do not hold for other types of equations we apply our results to draw geometric conclusions on conformal deformations of the mixed chern ricci forms a notion we introduced in the article our work is motivated by the close connections of these equations to problems in non kahler geometry and the fact that there have been increasing interests in fully nonlinear pde s beyond the complex monge ampere equation from complex geometry

collapsing of the chern ricci flow on elliptic surfaces we investigate the chern ricci flow an evolution equation of hermitian metrics generalizing the kahler ricci flow on elliptic bundles over a riemann surface of genus greater than one we show that starting at any gauduchon metric the flow collapses the elliptic fibers and the metrics converge to the pullback of a kahler einstein metric from the base some of our estimates are new even for the kahler ricci flow a consequence of our result is that on every minimal non kahler surface of kodaira dimension one the chern ricci flow converges in the sense of gromov hausdorff to an orbifold kahler einstein metric on a riemann surface

complex monge ampere equations and totally real submanifolds abstract we study the dirichlet problem for complex monge ampere equations in hermitian manifolds with general non pseudoconvex boundary our main result theorem 1 1 extends the classical theorem of caffarelli kohn nirenberg and spruck in c n we also consider the equation on compact manifolds without boundary attempting to generalize yau s theorems in the kahler case as applications of the main result we study some connections between the homogeneous complex monge ampere hcma equation and totally real submanifolds and a special dirichlet problem for the hcma equation related to donaldson s conjecture on geodesics in the space of kahler metrics

analysis of critical paths in a project network with fuzzy activity times abstract this paper proposes an approach to critical path analysis for a project network with activity times being fuzzy numbers in that the membership function of the fuzzy total duration time is constructed the basic idea is based on the extension principle and linear programming formulation a pair of linear programs parameterized by possibility level is formulated to calculate the lower and upper bounds of the fuzzy total duration time at by enumerating different values of the membership function of the fuzzy total duration time is constructed and the fuzzy critical paths are identified at the same time moreover by applying the yager ranking method definitions of the most critical path and the relative degree of criticality of paths are developed and these definitions are theoretically sound and easy to use in practice two examples with activity times being fuzzy numbers of l r and l l types discussed in previous studies are solved successfully to demonstrate the validity of the proposed approach since the total duration time is completely expressed by a membership function rather than by a crisp value the fuzziness of activity times is conserved completely and more information is provided for critical path analysis

on latest starting times and floats in activity networks with ill known durations abstract this paper deals with fuzzy activity networks where fuzzy intervals model uncertain durations of tasks while it is easy to compute fuzzy earliest starting times of activities using the critical path method the problem of determining latest starting dates and slack times is much more tricky and has never been solved in a fully satisfactory manner in the past here we propose a rigorous treatment of this problem in the framework of possibility theory the main difficulty lies in the fact that the behavior of latest starting dates and slack times as a function of task durations is not straightforward to predict for general network topologies however it is easier in the case of series parallel graphs the case of interval valued durations is first addressed and then extended to fuzzy intervals

transverse fully nonlinear equations on sasakian manifolds and applications abstract we prove a priori estimates for a class of transverse fully nonlinear equations on sasakian manifolds and give some geometric applications such as the transversion calabi yau theorem for transverse balanced and strongly gauduchon metrics we also explain that similar results hold on compact oriented taut transverse hermitian foliated manifold of complex co dimension n and give some geometric applications such as the transverse calabi yau theorems for transverse hermitian and strongly gauduchon metrics

stability and regularity of solutions of the monge ampere equation on hermitian manifolds abstract we prove stability of solutions of the complex monge ampere equation on compact hermitian manifolds when the right hand side varies in a bounded set in l p p 1 and it is bounded away from zero such solutions are shown to be holder continuous as an application we extend a recent result of szekelyhidi and tosatti on kahler einstein equation from kahler to hermitian manifolds

deformation limits of projective manifolds hodge numbers and strongly gauduchon metrics this paper is intended to start a series of works aimed at proving that if in a smooth complex analytic family of compact complex manifolds all the fibres except one are supposed to be projective then the remaining limit fibre must be moishezon a new method of attack whose starting point originates in demailly s work is introduced while we hope to be able to address the general case in the near future two important special cases are established here the one where the hodge numbers h0 1 of the fibres are supposed to be locally constant and the one where the limit fibre is assumed to be a strongly gauduchon manifold the latter is a rather weak metric assumption giving rise to a new rather general class of compact complex manifolds that we hereby introduce and whose relevance to this type of problems we underscore

new li yau hamilton inequalities for the ricci flow via the space time approach we prove li yau hamilton inequalties that extend hamilton s matrix inequality for solutions of the ricci flow with nonnegative curvature operators to obtain our extensions we apply the space time formalism of s c chu and one of the authors to solutions of the ricci flow modified by a cosmological constant then we adjoin to the ricci flow the evolution of a 1 form and a 2 form flowing by a system of heat type equations by a rescaling argument the inequalities we obtain in this manner yield new inequalities which are reminiscent of the linear trace inequality of hamilton and one of the authors

on the convergence of a modified kahler ricci flow we study the convergence of a modified kahler ricci flow defined by zhou zhang we show that the modified kahler ricci flow converges to a singular metric when the limit class is degenerate this proves a conjecture of zhang

the use of fuzzy variables in pert abstract in this paper we present a method called fpert for estimating a project completion time in the situation when activity duration times in the project network model are given in the form of fuzzy variables fuzzy sets on time space theoretical foundations of the method as well as results of calculations derived from a simple example are included

gauduchon metrics with prescribed volume form we prove that on any compact complex manifold one can find gauduchon metrics with prescribed volume form this is equivalent to prescribing the chern ricci curvature of the metrics and thus solves a conjecture of gauduchon from 1984

an upper bound on the expected completion time of pert networks abstract in this paper the problem of determining an upper bound on the expected project completion time described by the pert network is considered it is assumed that activity durations are independent random variables with given means the exact forms of probability distributions do not have to be known however their cumulative distribution functions are expected to belong to the so called nbue class very simple algorithms for deriving this bound are presented the computations can even be performed manually for more involved networks our approach producing a pessimistic evaluation of the expected value of the project duration extends considerably the information obtained through the use of the classical pert that always underestimates this value the results are illustrated by a simple example and errors of approximations are discussed

hessian measures ii in our previous paper on this topic we introduced the notion of k hessian measure associated with a continuous k convex function in a domain q in euclidean n space k 1 n and proved a weak continuity result with respect to local uniform convergence in this paper we consider k convex functions not necessarily continuous and prove the weak continuity of the associated k hessian measure with respect to convergence in measure the proof depends upon local integral estimates for the gradients of k convex functions

on a constant factor approximation for minmax regret problems using a symmetry point scenario abstract in order to find a robust solution under an unknown linear cost function it will be considered the minmax regret criterion it is assumed the vector of costs can take on values from a given uncertainty set the resulting optimization model has been extensively analyzed in the literature when the uncertain costs are modeled by closed intervals unfortunately except for rare applications this problem has np hard complexity which has led to the appearance of approximated methods seeking for good solutions in a short computational time the most recent approaches solve the deterministic version of the optimization problem under the midpoint scenario that realization in which each cost takes the midpoint of the closed interval proceeding in this way it can be obtained a 2 approximation for a wide class of minmax regret optimization models in this paper it is shown how this approach can be extended to a new class of minmax regret problems including more general uncertainty sets

dirichlet duality and the nonlinear dirichlet problem on riemannian manifolds in this paper we study the dirichlet problem for fully nonlin ear second order equations on a riemannian manifold as in our previous paper hl4 we define equations via closed subsets of the 2 jet bundle where each equation has a natural dual equation basic existence and uniqueness theorems are established in a wide variety of settings however the emphasis is on starting with a constant coefficient equation as a model which then universally determines an equation on every riemannian manifold which is equipped with a topological reduction of the structure group to the invariance group of the model for example this covers all branches of the homogeneous complex monge ampere equation on an almost complex hermitian manifold x in general for an equation f on a manifold x and a smooth domain x we give geometric conditions which imply that the dirichlet problem on is uniquely solvable for all continuous boundary functions we begin by introducing a weakened form of comparison which has the advantage that local implies global we then introduce two fundamental concepts the first is the notion of a monotonicity cone m for f if x carries a global m subharmonic function then weak comparison implies full compar ison the second notion is that of boundary f convexity which is defined in terms of the asymptotics of f and is used to define bar riers in combining these notions the dirichlet problem becomes uniquely solvable as claimed this article also introduces the notion of local affine jet equiva lence for subequations it is used in treating the cases above but gives results for a much broader spectrum of equations on manifolds including inhomogeneous equations and the calabi yau equation on almost complex hermitian manifolds a considerable portion of the paper is concerned with specific examples they include a wide variety of equations which make sense on any riemannian manifold and many which hold univer sally on almost complex or quaternionic hermitian manifolds or topologically calibrated manifolds

geometric flows and strominger systems a geometric flow on 2 2 forms is introduced which preserves the balanced condition of metrics and whose stationary points satisfy the anomaly equation in strominger systems the existence of solutions for a short time is established using hamilton s version of the nash moser implicit function theorem

the monge ampere equation on almost complex manifolds we study the dirichlet problem for the monge ampere equation on almost complex manifolds we obtain the existence of the unique smooth solution in strictly pseudoconvex domains

geometric plurisubharmonicity and convexity an introduction this is an essay on potential theory for geometric plurisubharmonic functions it begins with a given closed subset g of the grassmann bundle g p tx of tangent p planes to a riemannian manifold x this determines a nonlinear partial differential equation which is convex but never uniformly elliptic p dimx a surprising number of results in complex analysis carry over to this more general setting the notions of a g submanifold an upper semi continuous g plurisubharmonic function a g convex domain a g harmonic function and a g free submanifold are defined results include a restriction theorem as well as the existence and uniqueness of solutions to the dirichlet problem for g harmonic functions on g convex domains

fully non linear elliptic equations on compact hermitian manifolds we derive a priori estimates for solutions of a general class of fully non linear equations on compact hermitian manifolds our method is based on ideas that have been used for different specific equations such as the complex monge ampere hessian and inverse hessian equations as an application we solve a class of hessian quotient equations on kahler manifolds assuming the existence of a suitable subsolution the method also applies to analogous equations on compact riemannian manifolds