Year: 2013
Type: report
Abstract: We prove the existence of a unique maximal surface in an anti-de Sitter (AdS) convex Globally Hyperbolic Maximal (GHM) manifold with particles (i.e. with conical singularities along timelike lines) for cone-angles less than $\pi$. We reinterpret this result in terms of Teichm\"uller theory, and prove the existence of a unique minimal Lagrangian diffeomorphism isotopic to the identity between two hyperbolic structures with conical singularities of the same angles on a closed surface with marked points.
Author: Jérémy Toulisse
Institution: University of Luxembourg
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2202343969