Jean‐Marc Schlenker

collaborators

5 papers

math.GT2025

Volume functions and boundary data of 3-dimensional hyperbolic manifolds

Jean-Marc Schlenker

We review recent progress on two closely related sets of questions concerning convex co-compact hyperbolic manifolds, or convex domains in those manifolds, such as their convex cor…

math.GT2025

Projective rigidity of circle patterns and polyhedral surfaces in hyperbolic ends

Jean-Marc Schlenker

Let $S$ be a closed, orientable surface of genus $g \geq 2$ . We consider Delaunay circle patterns on $S$ equipped with a complex projective structure. We prove that the space of com…

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.DG2025

Weakly almost-Fuchsian manifolds are nearly-Fuchsian

Manh-Tien Nguyen, Jean-Marc Schlenker, Andrea Seppi

We show that a hyperbolic three-manifold $M$ containing a closed minimal surface with principal curvatures in $[- 1, 1]$ also contains nearby (non-minimal) surfaces with principal cu…

math.DG2024

Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes

Qiyu Chen, Jean-Marc Schlenker

Let $S$ be a closed surface of genus at least $2$ , let $h$ be a smooth metric of curvature $K < - 1$ on $S$ , and let $h_{0}$ be a hyperbolic metric on $S$ . We show that there exists a u…