Article Dans Une Revue Communications in Analysis and Geometry Année : 2024

Rigidity of Riemannian manifolds containing an equator

Laurent Mazet

Résumé

In this paper, we prove that a Riemannian $n$-manifold $M$ with sectional curvature bounded above by $1$ that contains a minimal $2$-sphere of area $4\pi$ which has index at least $n-2$ has constant sectional curvature $1$. The proof uses the construction of ancient mean curvature flows that flow out of a minimal submanifold. As a consequence we also prove a rigidity result for the Simon-Smith minimal spheres.

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Dates et versions

hal-02958594 , version 1 (05-06-2025)

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Laurent Mazet. Rigidity of Riemannian manifolds containing an equator. Communications in Analysis and Geometry, 2024, 32 (1), pp.21-63. ⟨10.4310/CAG.240905212306⟩. ⟨hal-02958594⟩
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