Strong Rigidity of Closed Minimal Hypersurfaces in Euclidean Spheres
Xu Han
TL;DR
This paper proves that closed minimal hypersurfaces in Euclidean spheres are strongly rigid, confirming longstanding conjectures and advancing understanding of their geometric properties.
Contribution
It establishes the strong rigidity of closed minimal hypersurfaces in spheres and confirms the Choi-Schoen and Chern conjectures for certain dimensions.
Findings
Confirmed strong rigidity of minimal hypersurfaces in spheres
Validated the Choi-Schoen conjecture
Validated the Chern conjecture for dimensions less than 7
Abstract
Let M be a closed embedded minimal hypersurface in a Euclidean sphere of dimension n+1, we prove that it is strongly rigid. As applications we confirm the conjecture proposed by Choi and Schoen in [3] and the Chern conjecture for n less than 7.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology