Roman Prosanov

activity

20182026

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5 papers · 1 filter

math.GT2025

Polyhedral surfaces in anti-de Sitter (2+1)-spacetimes

Roman Prosanov

We first prove that given a Fuchsian representation $ρ_\circ: π_1S \ra {\rm PSL}(2,\R)$, where $S$ is a closed oriented surface of genus $\geq 2$ , any hyperbolic cone-metric on $S$ …

math.GT2025

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…

math.GT2022

Hyperbolic 3-manifolds with boundary of polyhedral type

Roman Prosanov

Let $M$ 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-…

math.GT2020

Rigidity of compact Fuchsian manifolds with convex boundary

Roman Prosanov

A compact Fuchsian manifold with boundary is a hyperbolic 3-manifold homeomorphic to $S_{g} \times [0; 1]$ such that the boundary component $S_{g} \times {0}$ is geodesic. We prove…

math.GT2018

Ideal polyhedral surfaces in Fuchsian manifolds

Roman Prosanov

Let $S_{g, n}$ be a surface of genus $g > 1$ with $n > 0$ punctures equipped with a complete hyperbolic cusp metric. Then it can be uniquely realized as the boundary metric of an idea…