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The Anti-de Sitter Proof of Thurston’s Earthquake Theorem
Thurston’s earthquake theorem asserts that every orientation-preserving homeomorphism of the circle admits an extension to the hyperbolic plane which...
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Bulk-Boundary Correspondences and Unique Continuation in Asymptotically Anti-de Sitter Spacetimes
This article surveys the research presented by the author at the MATRIX Institute workshop Hyperbolic Differential Equations in Geometry and Physics...
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Counting orbits of certain infinitely generated non-sharp discontinuous groups for the anti-de Sitter space
Inspired by an example of Guéritaud and Kassel (Geom Topol 21(2):693–840, 2017), we construct a family of infinitely generated discontinuous groups
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Riemannian metrics on the moduli space of GHMC anti-de Sitter structures
We first extend the construction of the pressure metric to the deformation space of globally hyperbolic maximal Cauchy-compact anti-de Sitter...
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Fenchel–Nielsen coordinates on the augmented moduli space of anti-de Sitter structures
In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally...
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A class of inverse mean curvature type flows in the anti-de Sitter-Schwarzschild manifold
In this paper, we study the star-shaped hypersurfaces evolved by a class of inverse mean curvature type flows in the anti-de Sitter-Schwarzschild...
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Anti-de Sitter Geometry and Teichmüller Theory
The aim of this chapter is to provide an introduction to Anti-de Sitter geometry, with special emphasis on dimension three and on the relations with...
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In the Tradition of Thurston III Geometry and Dynamics
William Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding...
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Boundary metric of Epstein-Penner convex hull and discrete conformality
The Epstein-Penner convex hull construction associates to every decorated punctured hyperbolic surface a convex set in the Minkowski space. It works...
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Introduction: Wigner’s Elementary Systems in de Sitter (dS) Spacetime
This chapter offers readers an insight into the content of this book, including its motivations and methodology. It serves as a window that allows...
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A class of inverse quotient curvature flow in the AdS-Schwarzschild manifold
In this paper, we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold. We prove...
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Chern–Simons theory and cohomological invariants of representation varieties
We prove a general local rigidity theorem for pull-backs of homogeneous forms on reductive symmetric spaces under representations of discrete groups....