forgot password?
register here
Research articles
  search articles
  reviews guidelines
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
Members: 3630
Articles: 2'379'978
Articles rated: 2603

01 October 2023
  » arxiv » math/0511441

 Article overview

Minimal surfaces and particles in 3-manifolds
Kirill Krasnov ; Jean-Marc Schlenker ;
Date 17 Nov 2005
Subject Differential Geometry; Geometric Topology
AbstractWe use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit ``nice’’ foliations and explicit metrics, and whether the space of these metrics has a simple description in terms of Teichm"uller theory. In the hyperbolic settings both questions have positive answers for a certain subset of the quasi-Fuchsian manifolds: those containing a closed surface with principal curvatures at most 1. We show that this subset is parameterized by an open domain of the cotangent bundle of Teichm"uller space. These results are extended to ``quasi-Fuchsian’’ manifolds with conical singularities along infinite lines, known in the physics literature as ``massive, spin-less particles’’.
Things work better for globally hyperbolic anti-de Sitter manifolds: the parameterization by the cotangent of Teichm"uller space works for all manifolds. There is another description of this moduli space as the product two copies of Teichm"uller space due to Mess. Using the maximal surface description, we propose a new parameterization by two copies of Teichm"uller space, alternative to that of Mess, and extend all the results to manifolds with conical singularities along time-like lines. Similar results are obtained for de Sitter or Minkowski manifolds.
Finally, for all four settings, we show that the symplectic form on the moduli space of 3-manifolds that comes from parameterization by the cotangent bundle of Teichm"uller space is the same as the 3-dimensional gravity one.
Source arXiv, math/0511441
Services Forum | Review | PDF | Favorites   
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
of broad interest:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser CCBot/2.0 (
» my Online CV
» Free

News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2023 - Scimetrica