We prove a homogenization theorem for non-convex functionals depending on vector-valued functions, defined on Sobolev spaces with respect to oscillating measures. The proof combines the use of the localization methods of Γ-convergence with a ‘discretization’ argument, which allows to link the oscillating energies to functionals defined on a single Lebesgue space, and to state the hypothesis of ...

Suppose that N is a geometrically finite hyperbolic 3-manifold such that the bending locus of its convex core is a collection of simple closed curves α. We prove that the map which associates to each structure the lengths of the curves in the bending locus is a global diffeomorphism from the set of all structures bent along α onto its image. If α is maximal, the traces of the curves αi ∈ α are ...

The space of inequivalent representations of a compact surface S with χ(S) < 0 as a quotient of a convex domain in RP by a properly discontinuous group of projective transformations is a cell of dimension

Gromov and Thurston in [10] constructed, for each n 4, examples of compact n– manifolds which admit metrics of negative curvature, with arbitrarily small pinching constants, but do not admit metrics of constant curvature. We review these examples in Section 3. The main goal of this paper is to put convex projective structures on Gromov– Thurston examples. Suppose that  RP is an open subset and...

let $g=(v,e)$ be a simple graph. a set $dsubseteq v$ is adominating set of $g$ if every vertex in $vsetminus d$ has atleast one neighbor in $d$. the distance $d_g(u,v)$ between twovertices $u$ and $v$ is the length of a shortest $(u,v)$-path in$g$. an $(u,v)$-path of length $d_g(u,v)$ is called an$(u,v)$-geodesic. a set $xsubseteq v$ is convex in $g$ ifvertices from all $(a, b)$-geodesics belon...

let $g=(v,e)$ be a simple graph. a set $dsubseteq v$ is adominating set of $g$ if every vertex in $vsetminus d$ has atleast one neighbor in $d$. the distance $d_g(u,v)$ between twovertices $u$ and $v$ is the length of a shortest $(u,v)$-path in$g$. an $(u,v)$-path of length $d_g(u,v)$ is called an$(u,v)$-geodesic. a set $xsubseteq v$ is convex in $g$ ifvertices from all $(a, b)$-geodesics belon...

We consider a class of integer-valued discrete convex functions, called BS-convex functions, defined on integer lattices whose affinity domains are sets of integral points of integral bisubmodular polyhedra. We examine discrete structures of BSconvex functions and give a characterization of BS-convex functions in terms of their convex conjugate functions by means of (discordant) Freudenthal sim...