A word hyperbolic group G is called GFERF if every quasiconvex subgroup coincides with the intersection of finite index subgroups containing it. We show that in any such group, the product of finitely many quasiconvex subgroups is closed in the profinite topology on G.

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer–Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The “local” proof strategy combines blow-up arguments with the singular...

This paper explores some connections between rank one convexity, multiplicative quasiconvexity and Schur convexity. Theorem 5.1 gives simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant. Theorem 6.2 describes a class of non-polyconvex but multiplicative quasiconvex isotropic functions. Relevance of...

A result of Larsen concerning the structure of the approximate gradient of certain sequences of functions with Bounded Variation is used to present a short proof of Ambrosio’s lower semicontinuity theorem for quasiconvex bulk energies in SBV . It enables to generalize to the SBV setting the decomposition lemma for scaled gradients in dimension reduction and also to show that, from the point of ...

We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints such that all functions are, at least, Dini differentiable (in some cases, Hadamard differentiable and sometimes, quasiconvex). Several constraint qualifications are given in such a way that generalize both the qualifications introduced by Maeda and the classical ones, when the f...

We study some classes of generalized convex functions, using a generalized derivative approach. We establish some links between these classes and we devise some optimality conditions for constrained optimization problems. In particular, we get Lagrange-Kuhn-Tucker multipliers for mathematical programming problems. Key words: colinvex, colin…ne, generalized derivative, mathematical programming, ...

A geodesic metric space X is called hyperbolic if there exists δ ≥ 0 such that every geodesic triangle ∆ in X is δ-slim, i.e., each side of ∆ is contained in a closed δ-neighborhood of the two other sides. Let G be a group generated by a finite set A and let Γ(G,A) be the corresponding Cayley graph. The group G is said to be word hyperbolic if Γ(G,A) is a hyperbolic metric space. A subset Q of ...

The space of C-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains is considered. The investigation of the dimension of the spaces of biquintic and bisixtic C-smooth geometrically continuous isogeometric functions on such domains is presented. In addition, C-smooth isogeometric functions are constructed to be used for performing L-approximation a...