We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties the such as whether it is quasiconvex, normal, finite-index or torsion-free.We use show that reflection subgroups are one-ended 2-dimensional RACG. provide an algorithm determines given one-ended, RACG isomorphic some another In addition, we answer s...

We analyze the semiconvex hulls of the subset K in symmetric matrices given by K = fF 2 M 22 : F T = F; jF 11 j = a; jF 12 j = b; jF 22 j = cg that was rst considered by Dacorogna&Tanteri Commun. in PDEs 2001]. We obtain explicit formulae for the polyconvex, the quasiconvex, and the rank-one convex hull for ac ? b 2 0 and show in particular that the quasiconvex and the polyconvex hull are diier...

We provide an explicit description of the convex hull of the set of matrices of bounded rank, restricted to balls for the spectral norm. As applications, we deduce two relaxed forms of the rank function restricted to balls for the spectral norm: one is the quasiconvex hull of this rank function, another one is the convex hull of the rank function, thus retrieving Fazel's theorem (2002). Key-wor...

The relation between quasiconvexity and k-quasiconvexity, k ≥ 2, is investigated. It is shown that every smooth strictly k-quasiconvex integrand with p-growth at infinity, p > 1, is the restriction to k-th order symmetric tensors of a quasiconvex function with the same growth. When the smoothness condition is dropped, it is possible to prove an approximation result. As a consequence, lower semi...

We prove that certain compact cube complexes have special finite covers. This means they have finite covers whose fundamental groups are quasiconvex subgroups of right-angled Artin groups. As a result we obtain linearity and the separability of quasiconvex subgroups for the groups we consider. Our result applies, in particular, to a compact negatively curved cube complex whose hyperplanes do no...

We define a group to be translation discrete if it carries a metric in which the translation numbers of the non-torsion elements are bounded away from zero. We define the notion of quasiconvex space which generalizes the notion of both CAT(0) and Gromov–hyperbolic spaces. We show that a cocompact group of isometries acting properly discontinuously cocompactly on a proper quasiconvex metric spac...

Abstract. A BDDC (balancing domain decomposition by constraints) algorithm is developed for elasticity problems in three dimensions with mortar discretization on geometrically nonconforming subdomain partitions. Coarse basis functions in the BDDC algorithm are constructed from primal constraints on faces. These constrains are similar to the average matching condition and the moment matching con...

For a fixed word hyperbolic group we compare different residual properties related to quasiconvex subgroups.