Level Curves of Minimal Graphs
Allen Weitsman

TL;DR
This paper establishes a curvature inequality for level sets of minimal graphs with zero boundary conditions and demonstrates that boundary concavity implies all level sets are concave.
Contribution
It introduces a new inequality relating curvature of level sets to boundary conditions and proves concavity of level sets under boundary concavity.
Findings
Curvature inequality for minimal graph level sets
Concavity of level sets when boundary is concave
All level sets are concave if boundary is concave
Abstract
We prove an inequality for the curvature of level sets of minimal graphs having vanishing boundary values and show that if the boundary is concave, then all the level sets are concave.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Computational Geometry and Mesh Generation
