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arXiv · 2010.01994

Rigidity of riemannian manifolds containing an equator

Laurent Mazet
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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.

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Laurent Mazet. 2020-10-05. Rigidity of riemannian manifolds containing an equator. https://doi.org/10.4310/cag.240905212306

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