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arXiv · 2301.02932

Index of minimal hypersurfaces in real projective spaces

Shuli Chen
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Abstract

We prove that for an embedded unstable one-sided minimal hypersurface of the $(n+1)$-dimensional real projective space, the Morse index is at least $n+2$, and this bound is attained by the cubic isoparametric minimal hypersurfaces. We also show that there exist closed embedded two-sided minimal surfaces in the 3-dimensional real projective space of each odd index by computing the index of the Lawson surfaces.

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Shuli Chen. 2023-01-07. Index of minimal hypersurfaces in real projective spaces. https://doi.org/10.1093/imrn%2Frnad312

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