On Chernʼs problem for rigidity of minimal hypersurfaces in the spheres

2011/02/02 by Qi Ding, Y. L. Xin, Y.L. Xin · 51 citations
Mathematics · #Combinatorics #Constant (computer programming) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Hypersurface #Mathematical analysis #Mathematics #Mean curvature #Physics #Pure mathematics #Quantum mechanics #Rigidity (electromagnetism) #SPHERES #Second fundamental form

paper · pdf · doi:10.1016/j.aim.2011.01.018

published in Advances in Mathematics 227(1), 131-145 (Elsevier BV)

openalex publication_date 2011/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Citations

• Local Rigidity Theorems for Minimal Hypersurfaces
• Minimal Varieties in Riemannian Manifolds

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• A new characterization of the Clifford torus via scalar curvature pinching
• A lower bound for L₂ length of second fundamental form on minimal hypersurfaces
• A new pinching theorem for complete self-shrinkers and its generalization
• Ancient solutions to mean curvature flow for isoparametric submanifolds
• Classification and rigidity of self-shrinkers in the Mean curvature flow
• Chern conjecture on minimal hypersurfaces
• On embedded minimal hypersurfaces in Sⁿ⁺¹ with symmetries
• The Rigidity Theorems for Self-Shrinkers in the Mean Curvature Flow