Hausdorff measure of quasicircles

István Prause, Xavier Tolsa, Ignacio Uriarte-Tuero

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

S. Smirnov (2010) [10] proved recently that the Hausdorff dimension of any K-quasicircle is at most 1+k2, where k=(K-1)/(K+1). In this paper we show that if Γ is such a quasicircle, then H1+k2(B(x,r)∩Γ)≤C(k)r1+k2 for all x ∈C{double-struck}, r>0, where Hs stands for the s-Hausdorff measure. On a related note we derive a sharp weak-integrability of the derivative of the Riemann map of a quasidisk. © 2011 Elsevier Inc.
Original languageEnglish
Pages (from-to)1313-1328
JournalAdvances in Mathematics
Volume229
Issue number2
DOIs
Publication statusPublished - 30 Jan 2012

Keywords

  • Hausdorff measure
  • Quasiconformal mappings in the plane

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