On δ-Stable Minimal Hypersurfaces in Rn+1

Abstract

In this paper, we extend several results established for stable minimal hypersurfaces to δ-stable minimal hypersurfaces. These include the regularity and compactness theorems for immersed δ-stable minimal hypersurfaces in Rn+1 when n3 and δ>n2n, as well as the δ-stable Bernstein theorem for n=3 and n=4 for properly immersion. The range of δ is optimal, as the n-dimensional catenoid in Rn+1 is n2n-stable.

Publication
Submitted. 2407.03222, 2024
Gaoming Wang
Gaoming Wang
PostDoc

My research interests include Geometric Analysis and Partial Differential Equations.