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Preprints, Working Papers, ... Year : 2020

Rigidity of Riemannian manifolds containing an equator

Laurent Mazet

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. As a consequence we also prove a rigidity result for the Simon-Smith minimal spheres.

Dates and versions

hal-02958594 , version 1 (06-10-2020)

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