# Rigidity of riemannian manifolds containing an equator

Abstract : 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.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-02958594
Contributor : Laurent Mazet <>
Submitted on : Tuesday, October 6, 2020 - 9:33:43 AM
Last modification on : Thursday, October 15, 2020 - 9:47:39 AM

### Identifiers

• HAL Id : hal-02958594, version 1
• ARXIV : 2010.01994

### Citation

Laurent Mazet. Rigidity of riemannian manifolds containing an equator. 2020. ⟨hal-02958594⟩

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