Symmetry of hypersurfaces with ordered mean curvature in one direction

2019/10/10 by Yanyan Li, Li, Yanyan, Xukai Yan +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1910.04348

openalex publication_date 2019/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

For a connected n-dimensional compact smooth hypersurface M without boundary embedded in ℝⁿ⁺¹, a classical result of Aleksandrov shows that it must be a sphere if it has constant mean curvature. Li and Nirenberg studied a one-directional analog of this result: if every pair of points (x',a), (x',b)∈ M with a<b></b>

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