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

• DOI: 10.2140/pjm.2014.267.489
• Publication Date: 2014-05-17T15:48:51Z
• Authors: Pei-he Wang
• Keywords: Minimal surface; Gaussian curvature

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