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arXiv · 2201.06154

Min-max minimal hypersurfaces with higher multiplicity

Zhichao Wang·Xin Zhou
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Abstract

We exhibit the first set of examples of non-bumpy metrics on the $(n+1)$-sphere ($2\leq n\leq 6$) in which the varifold associated with the two-parameter min-max construction must be a multiplicity-two minimal $n$-sphere. This is proved by a new area-and-separation estimate for certain minimal hypersurfaces with Morse index two inspired by an early work of Colding-Minicozzi. We also construct non-bumpy projective spaces in which the first min-max hypersurfaces are one-sided, and non-bumpy balls in which the free boundary min-max hypersurfaces are improper.

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Zhichao Wang, Xin Zhou. 2022-01-16. Min-max minimal hypersurfaces with higher multiplicity. https://arxiv.org/abs/2201.06154

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