Related papers: Anti-de Sitter geometry and Teichm\"uller theory

This is a commentary on Teichm\"ullers' paper "Ver\"anderliche Riemannsche Fl\"achen" (Variable Riemann Surfaces), published in 1944. This paper is the last one that Teichm\"uller wrote on the problem of moduli. At most places the paper…

The geometric structure of the null solutions of de Sitter D=5 gauged supergravity coupled to vector multiplets is investigated. These solutions are Kundt metrics, constructed from a one-parameter family of three dimensional Gauduchon-Tod…

We discuss some of the issues that arise when considering the physics of asymptotically de Sitter spacetimes, and attempts to address them. Our development begins at the classical level, where several initial value problems are discussed,…

Let $S$ be an orientable surface with negative Euler characteristic. For $k \in \mathbb{N}$, let $\mathcal{C}_{k}(S)$ denote the $\textit{k-curve graph}$, whose vertices are isotopy classes of essential simple closed curves on $S$, and…

We present an outline of the theory of universal Teichmuller space, viewed as part of the theory of QS, the space of quasisymmetric homeomorphisms of a circle. Although elements of QS act in one dimension, most results depend on a…

We study the Teichm\"uller metric on the Teichm\"uller space of a surface of finite type, in regions where the injectivity radius of the surface is small. The main result is that in such regions the Teichm\"uller metric is approximated up…

This thesis is organized as follows. In Chapter 2, some preliminaries are given on isometries and conformal symmetries, and we become familiar with the Virasoro algebra. Two examples of classical central charges are discussed. Chapter 3…

We consider the Grothendieck--Teichm\"uller group under a new aspect. Using real algebraic geometry and web theory we show that it preserves dihedral symmetry relations, present in the fundamental groupoids of configuration spaces of marked…

This is an introduction to the algebraic aspect of Teichm\"uller dynamics, with a focus on its interplay with the geometry of moduli spaces of curves as well as recent advances in the field.

Consider a 3$-$dimensional manifold $N$ obtained by gluing a finite number of ideal hyperbolic tetrahedra via isometries along their faces. By varying the isometry type of each tetrahedron but keeping fixed the gluing pattern we define a…

In this paper, we give a framework for the study of the extremal length geometry of Teichm\"uller space after S. Kerckhoff, F. Gardiner and H. Masur. There is a natural compactification using extremal length geometry introduced by Gardiner…

We obtain a class of exact solutions representing null particles moving in three-dimensional (anti-) de Sitter spaces by boosting the corresponding static point source solutions given by Deser and Jackiw. In de Sitter space the resulting…

We consider new cosmological solutions which generalize the cosmological patch of the Anti-de Sitter (AdS) space-time, allowing for fluids with equations of state such that $w\neq -1$. We use them to derive the associated full manifolds. We…

Suppose a one-dimensional isometry group acts on a space, we can consider a submergion induced by the isometry, namely we obtain an orbit space by identification of points on the orbit of the group action. We study the causal structure of…

We give a definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We present the results of gr-qc/0110014 which show that our…

In this paper we provide a family of algebraic space-like surfaces in the three dimensional anti de Sitter space that shows that this Lorentzian manifold admits algebraic maximal examples of any order. Then, we classify all the space-like…

We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 3. This inequality generalizes the classical Minkowski inequality for surfaces in the three…

We classify solutions of 10d type IIA/B supergravities with orientifolds, on a 4d maximally symmetric spacetime times a 6d group manifold. We then look for new solutions in previously unexplored solution classes, and find some: (anti-) de…

This is a commentary on Teichm{\"u}ller's paper Ein Verschiebungssatz der quasikonformen Abbildung (A displacement theorem of quasiconformal mapping), published in 1944. We explain in detail how Teichm{\"u}ller solves the problem of finding…

We develop further previous work on de Sitter extremal surfaces and time entanglement structures in quantum mechanics. In the first part, we first discuss explicit quotient geometries. Then we construct smooth bulk geometries with replica…