Convexity of level sets and a two-point function

Ben Weinkove*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We establish a maximum principle for a two-point function in order to analyze the convexity of level sets of harmonic functions. We show that this can be used to prove a strict convexity result involving the smallest principal curvature of the level sets.

Original languageEnglish (US)
Pages (from-to)499-509
Number of pages11
JournalPacific Journal of Mathematics
Volume295
Issue number2
DOIs
StatePublished - 2018

Keywords

  • Convexity
  • Harmonic functions
  • Level sets
  • Maximum principle
  • Principal curvature
  • Two point function

ASJC Scopus subject areas

  • Mathematics(all)

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