forgot password?
register here
Research articles
  search articles
  reviews guidelines
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
Members: 2997
Articles: 2'060'055
Articles rated: 2581

12 April 2021
  » arxiv » 0708.2371

 Article overview

Singularities of quadratic differentials and extremal Teichm"{u}ller mappings defined by Dehn twist
Chaohui Zhang ;
Date 17 Aug 2007
AbstractLet $S$ be a Riemann surface of type $(p,n)$ with $3p-3+n>0$. Let $omega$ be a pseudo-Anosov map of $S$ that is obtained from Dehn twists along two families ${A,B}$ of simple closed geodesics that fill $S$. Then $omega$ can be realized as an extremal Teichm"{u}ller mapping on a surface of type $(p,n)$ which is also denoted by $S$. Let $phi$ be the corresponding holomorphic quadratic differential on $S$. In this paper, we compare the locations of some distinguished points on $S$ in the $phi$-flat metric to their locations with respect to the complete hyperbolic metric. More precisely, we show that all possible non-puncture zeros of $phi$ must stay away from all closures of once punctured disk components of $Sackslash {A, B}$, and the closure of each disk component of $Sackslash {A, B}$ contains at most one zero of $phi$. As a consequence of the result, we assert that the number of distinct zeros and poles of $phi$ is less than or equal to the number of components of $Sackslash {A, B}$.
Source arXiv, 0708.2371
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 © 2005-2021 - Scimetrica