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arXiv · 1803.08735

Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces

Claudio Gorodski·Ricardo A. E. Mendes·Marco Radeschi
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Abstract

We find many examples of compact Riemannian manifolds $(M,g)$ whose closed minimal hypersurfaces satisfy a lower bound on their index that is linear in their first Betti number. Moreover, we show that these bounds remain valid when the metric $g$ is replaced with $g'$ in a neighbourhood of $g$. Our examples $(M,g)$ consist of certain minimal isoparametric hypersurfaces of spheres; their focal manifolds; the Lie groups $SU(n)$ for $n\leq 17$, and $Sp(n)$ for all $n$; and all quaternionic Grassmannians.

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Claudio Gorodski, Ricardo A. E. Mendes, Marco Radeschi. 2018-03-23. Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces. https://arxiv.org/abs/1803.08735

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