Quasisymmetric spheres over Jordan domains

Vyron Vellis, Jang Mei Wu

Research output: Contribution to journalArticlepeer-review

Abstract

Let Ω be a planar Jordan domain. We consider double-dome-like surfaces Σ defined by graphs of functions of dist(·, ∂Ω) over Ω. The goal is to find the right conditions on the geometry of the base Ω and the growth of the height so that Σ is a quasisphere or is quasisymmetric to S2. An internal uniform chord-arc condition on the constant distance sets to ∂Ω, coupled with a mild growth condition on the height, gives a close-to-sharp answer. Our method also produces new examples of quasispheres in Rn, for any n ≥ 3.

Original languageEnglish (US)
Pages (from-to)5727-5751
Number of pages25
JournalTransactions of the American Mathematical Society
Volume368
Issue number8
DOIs
StatePublished - 2016

Keywords

  • Double-dome-like surfaces
  • Level chord-arc property
  • Quasispheres
  • Quasisymmetric spheres

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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