On stable hypersurfaces with constant mean curvature in Euclidean spaces

2012/12/14 by Jinpeng Lu, Lu, Jinpeng · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1212.3427

openalex publication_date 2012/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive curvature estimates for strongly stable hypersurfaces with constant mean curvature immersed in ℝⁿ⁺¹, which show that the locally controlled volume growth yields a globally controlled volume growth if ∂ M=∅. Moreover, we deduce a Bernstein-type theorem for complete stable hypersurfaces with constant mean curvature of arbitrary dimension, given a finite L^p-norm curvature condition.

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• Scale-Separated Curvature Estimates for Strongly Stable Hypersurfaces

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