Vol. 295, No. 2, 2018

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Convexity of level sets and a two-point function

Ben Weinkove

Vol. 295 (2018), No. 2, 499–509
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, two point function, level sets, principal curvature, maximum principle, harmonic functions
Mathematical Subject Classification 2010
Primary: 31B05, 35J05
Milestones
Received: 21 February 2017
Revised: 11 September 2017
Accepted: 9 January 2018
Published: 11 April 2018
Authors
Ben Weinkove
Department of Mathematics
Northwestern University
Evanston, IL
United States