Convexity of level sets and a two-point function

Ben Weinkove

doi:10.2140/pjm.2018.295.499

Convexity of level sets and a two-point function

Ben Weinkove^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

6 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 language	English (US)
Pages (from-to)	499-509
Number of pages	11
Journal	Pacific Journal of Mathematics
Volume	295
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2018.295.499
State	Published - 2018

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.2140/pjm.2018.295.499

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title = "Convexity of level sets and a two-point function",

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.",

keywords = "Convexity, Harmonic functions, Level sets, Maximum principle, Principal curvature, Two point function",

author = "Ben Weinkove",

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KW - Harmonic functions

KW - Level sets

KW - Maximum principle

KW - Principal curvature

KW - Two point function

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Convexity of level sets and a two-point function

Abstract

Keywords

ASJC Scopus subject areas

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