Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...
We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group GG associated with nonsingular GG-spaces. We deduce that any two boundary representations of a hyperbolic locally ...
The work is about the study of group representations in the group of isometries of a separable complex hyperbolic space. The main part is the classification of the representations of the group of isometries of a finite dimensional complex hyperbolic spa ...
This thesis is a study of the global well-posedness of the Cauchy problems for half-wave maps from the Minkowski space of dimension n+1 to the 2-dimensional sphere and the hyperbolic plane. The work is mainly based on the results from Krieger-Sire 17' in ...
When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...
We prove that the real cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective sp ...
A strong coupling of the lattice to functional properties is observed in many transition metal oxide systems, such as the ABO(3) perovskites. In the quest for tailor-made materials, it is essential to be able to control the structural properties of the com ...
The current information landscape is characterised by a vast amount of relatively semantically homogeneous, when observed in isolation, data silos that are, however, drastically semantically fragmented when considered as a whole. Within each data silo, inf ...
In this study, based on multipole expansion method an analytical treatment is presented for the anti-plane scattering of SH-waves by an arbitrarily oriented elliptic cavity/crack which is embedded near the interface between exponentially graded and homogen ...
Let M be a quotient of H-2 x ... x H-2 (product of hyperbolic planes) by a uniform lattice of. PSL2(R))(n). We prove that, among metrics of M of prescribed volume, the sum of hyperbolic metrics has minimal volume entropy. ...
Bi-Jacobi fields are generalized Jacobi fields, and are used to efficiently compute approximations to Riemannian cubic splines in a Riemannian manifold M. Calculating bi-Jacobi fields is straightforward when M is a symmetric space such as bi-invariant SO(3 ...
Representations of solutions of equations describing the diffusion and quantum dynamics of particles in a Riemannian manifold are discussed under the assumption that the mass of particles is anisotropic and depends on both time and position. These equation ...
Let Isom(H^n) be the group of isometries of the n-dimensional real hyperbolic space. We first classify all continuous non-elementary actions of on the infinite-dimensional real hyperbolic space. We then prove the existence of a continuous family of non-iso ...
We generalize to a wider class of hyperbolic groups a construction by Misha Kapovich yielding convex cocompact representations into real hyperbolic space. ...
Let X be a (not-necessarily homotopy-associative) H-space. We show that TCn+1(X) = cat(X-n), for n >= 1, where TCn+1(-) denotes the so-called higher topological complexity introduced by Rudyak, and cat(-) denotes the Lusternik-Schnirelmann category. We als ...
Poincaré's uniformisation theorem says that any Riemann surface is conformally equivalent to a unique (up to isometry) surface of constant Gauss curvature 0, 1 or –1. The (topologically) richest of these three worlds is for curvature –1 formed of hyperboli ...
The objective of this PhD thesis is the approximate computation of the solutions of the Spectral Problem associated with the Laplace operator on a compact Riemann surface without boundaries. A Riemann surface can be seen as a gluing of portions of the Hype ...
It is shown that 2-dimensional subdivisions can be made regular by moving their vertices within parallel 1-dimensional spaces. As a consequence, any 2-dimensional subdivision is projected from the boundary complex of a 4-polytope. ...
We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained after a detour throu ...
