The Concavity of the Gaussian Curvature of the convex level sets of minimal surface with respect to the height

Details The Concavity of the Gaussian Curvature of the convex level sets of minimal surface with respect to the height The Concavity of the Gaussian Curvature of the convex level sets of minimal surface with respect to the height

2011-01-17

arxiv.org/abs/1101.3196v2

Mathematics

Analysis of PDEs

Scientific paper

For the minimal graph with strict 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.

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