The concavity of the Gaussian curvature of the convex level sets of minimal surfaces with respect to the height

Pei-he Wang

Vol. 267 (2014), No. 2, 489–509

DOI: 10.2140/pjm.2014.267.489

Abstract

For the minimal graph with strictly convex level sets, we find an auxiliary function to study the Gaussian curvature of the level sets. We prove that this curvature function is a concave function with respect to the height of the minimal surface while this auxiliary function is almost sharp when the minimal surface is the catenoid.

Keywords

concavity, minimal surface, Gaussian curvature, level sets

Mathematical Subject Classification 2010

Primary: 35B45

Milestones

Received: 16 February 2012

Revised: 10 June 2013

Accepted: 23 September 2013

Published: 11 May 2014