Convexity of Level Sets of Minimal Graph on Space Form with Nonnegative Curvature

TL;DR

This paper proves the regularity and strict convexity of level sets of minimal graphs on convex rings within space forms of nonnegative curvature, using the continuity method.

Contribution

It establishes the convexity properties of minimal graph level sets in nonnegative curvature space forms, extending understanding of geometric PDEs.

Findings

Level sets are regular and strictly convex.

Results apply to minimal graphs on convex rings.

Uses the continuity method for proofs.

Abstract

For the minimal graph defined on a convex ring in the space form with nonnegative curvature, we obtain the regularity and the strict convexity about its level sets by the continuity method.