Convex Shapes and Harmonic Caps

Laura DeMarco*, Kathryn Lindsey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Any planar shape P⊂ C can be embedded isometrically as part of the boundary surface S of a convex subset of R3 such that ∂P supports the positive curvature of S. The complement Q= S\ P is the associated cap. We study the cap construction when the curvature is harmonic measure on the boundary of (C^ \ P, ∞). Of particular interest is the case when P is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy.

Original languageEnglish (US)
Pages (from-to)97-117
Number of pages21
JournalArnold Mathematical Journal
Issue number1
StatePublished - Apr 1 2017


  • Convex shape
  • Curvature
  • Harmonic measure
  • Julia set
  • Polyhedra

ASJC Scopus subject areas

  • General Mathematics


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