Ber's constants for punctured spheres and hyperelliptic surfaces

Florent Balacheff, Hugo Parlier*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

The main goal of this paper is to present a proof of Buser's conjecture about Bers' constants for spheres with cusps (or marked points) and for hyperelliptic surfaces. More specifically, our main result states that any hyperbolic sphere with n cusps has a pants decomposition with all of its geodesics of length bounded by 30√2π(n-2). Other results include lower and upper bounds for Bers' constants for hyperelliptic surfaces and spheres with boundary geodesics.

Original languageEnglish
Pages (from-to)271-296
Number of pages26
JournalJournal of Topology and Analysis
Volume4
Issue number3
DOIs
Publication statusPublished - Sep 2012

Keywords

  • Bers' constants
  • Riemann surfaces
  • simple closed geodesics
  • Teichmüller and moduli spaces

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