Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials

Research output: Contribution to journalArticleScientificpeer-review

Details

Original languageEnglish
Pages (from-to)229-245
Number of pages17
JournalJOURNAL D ANALYSE MATHEMATIQUE
Volume132
Issue number1
Publication statusPublished - 29 Jun 2017
MoE publication typeA1 Journal article-refereed

Researchers

Research units

  • University of Manitoba
  • Uppsala University

Abstract

Let Σ be a Riemann surface of genus g bordered by n curves homeomorphic to the circle S1. Consider quasiconformal maps f: Σ→Σ1 such that the restriction to each boundary curve is a Weil-Petersson class quasisymmetry. We show that any such f is homotopic to a quasiconformal map whose Beltrami differential is L2 with respect to the hyperbolic metric on Σ. The homotopy H(t, •): Σ → Σ1 is independent of t on the boundary curves; that is, H(t, p) = f(p) for all p ∈ ∂Σ.

ID: 14489133