Roman Prosanov

activity

20182026

collaborators

11 papers

math.DG2026

On $(2, 1)$ -dimensional anti-de Sitter spacetimes with convex boundary

Roman Prosanov, Jean-Marc Schlenker, Graham Andrew Smith

Let $S$ be a closed oriented surface of genus at least $2$ . Let $X$ be a $(2, 1)$ -dimensional anti-de Sitter spacetime homeomorphic to $S \times [- 1, 1]$ with smooth, spacelike, strong…

math.MG2026

Second-order rigidity of coned polytope frameworks and the stress-flex conjecture from a vector-valued Schläfli formula

Eleni Pachyli, Roman Prosanov, Martin Winter

A coned polytope framework (CPF) is the bar-joint framework obtained from the 1-skeleton of a convex polytope by coning over some interior point. It was recently shown that CPFs ar…

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.MG2023

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 $h$ on a closed surface $S$ , any flat metric on $S$ with negative singular curvatures isometrically embeds as a convex polyhedral Cauc…

math.MG2023

Prescribed curvature problem for discrete conformality on convex spherical cone-metrics

Ivan Izmestiev, Roman Prosanov, Tianqi Wu

Let $S$ be the 2-sphere and $V \subset S$ be a finite set of at least three points. We show that for each function $κ : V \to (0, 2 π)$ satisfying elementary necessary condit…

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.DG2022

New invariants of Gromov-Hausdorff limits of Riemannian surfaces with curvature bounded below

Semyon Alesker, Mikhail Katz, Roman Prosanov

Let ${X_{i}}$ be a sequence of compact $n$ -dimensional Alexandrov spaces (e.g. Riemannian manifolds) with curvature uniformly bounded below which converges in the Gromov-Hausdorff…

math.MG2022

Dual metrics on the boundary of strictly polyhedral hyperbolic 3-manifolds

Roman Prosanov

Let $M$ be a compact oriented 3-manifold with non-empty boundary consisting of surfaces of genii $> 1$ such that the interior of $M$ is hyperbolizable. We show that for each spheric…

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…

On (2,1)-dimensional anti-de Sitter spacetimes with convex boundary

Second-order rigidity of coned polytope frameworks and the stress-flex conjecture from a vector-valued Schläfli formula

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

Rigidity of anti-de Sitter (2+1)-spacetimes with convex boundary near the Fuchsian locus

Polyhedral surfaces in flat (2+1)-spacetimes and balanced cellulations on hyperbolic surfaces

Prescribed curvature problem for discrete conformality on convex spherical cone-metrics

Hyperbolic 3-manifolds with boundary of polyhedral type

New invariants of Gromov-Hausdorff limits of Riemannian surfaces with curvature bounded below

Dual metrics on the boundary of strictly polyhedral hyperbolic 3-manifolds

Rigidity of compact Fuchsian manifolds with convex boundary

Ideal polyhedral surfaces in Fuchsian manifolds

On $(2, 1)$ -dimensional anti-de Sitter spacetimes with convex boundary