Index estimate by first Betti number of minimal hypersurfaces in compact symmetric spaces

Toru Kajigaya; Keita Kunikawa

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arXiv · 2410.11585

Index estimate by first Betti number of minimal hypersurfaces in compact symmetric spaces

Toru Kajigaya·Keita Kunikawa

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Abstract

We show that the Morse index of unstable closed minimal hypersurface $\Sigma$ in a compact semi-simple Riemannian symmetric space $M=G/K$ is bounded from below by constant times the first Betti number of $\Sigma$. Our proof is based on a natural extension of the previous method and this also provides a novel approach for the index estimate.

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BibTeX RIS

Toru Kajigaya, Keita Kunikawa. 2024-10-15. Index estimate by first Betti number of minimal hypersurfaces in compact symmetric spaces. https://arxiv.org/abs/2410.11585

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