From the 1 of 6 linked papers with an AI index.
6 papers
Second-order rigidity of coned polytope frameworks and the stress-flex conjecture from a vector-valued Schläfli formula
Eleni Pachyli, Roman Prosanov, Martin Winter
The paper proves that coned polytope frameworks are second‑order rigid by introducing the Wachspress stress and resolving the stress‑flex conjecture using a discrete‑geometric vers…
Rigidity of anti-de Sitter (2+1)-spacetimes with convex boundary near the Fuchsian locus
Roman Prosanov, Jean-Marc Schlenker
We prove that globally hyperbolic compact anti-de Sitter (2+1)-spacetimes with strictly convex spacelike boundary that is either smooth or polyhedral and whose holonomy is close to…
Polyhedral surfaces in anti-de Sitter (2+1)-spacetimes
Roman Prosanov
We first prove that given a Fuchsian representation $Ï_\circ: Ï_1S \ra {\rm PSL}(2,\R)$, where is a closed oriented surface of genus , any hyperbolic cone-metric on $…
Polyhedral surfaces in flat (2+1)-spacetimes and balanced cellulations on hyperbolic surfaces
François Fillastre, Roman Prosanov
We first prove that given a hyperbolic metric on a closed surface , any flat metric on with negative singular curvatures isometrically embeds as a convex polyhedral Cauc…
Dual metrics on the boundary of strictly polyhedral hyperbolic 3-manifolds
Roman Prosanov
Let be a compact oriented 3-manifold with non-empty boundary consisting of surfaces of genii such that the interior of is hyperbolizable. We show that for each spheric…
Hyperbolic 3-manifolds with boundary of polyhedral type
Roman Prosanov
Let be a compact orientable 3-manifold with hyperbolizable interior and non-empty boundary such that all boundary components have genii at least 2. We study an Alexandrov-Weyl-…