Convexity of level sets and a two-point function

Ben Weinkove

Vol. 295 (2018), No. 2, 499–509

DOI: 10.2140/pjm.2018.295.499

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