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arXiv · 2008.04425

Locally Maximizing Metric of Width on Manifolds with Boundary

Yucheng Tu
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Abstract

In this paper we use min-max theory to study the existence free boundary minimal hypersurfaces (FBMHs) in compact manifolds with boundary $(M^{n+1}, \partial M, g)$, where $2\leq n\leq 6$. Under the assumption that $g$ is a local maximizer of the width of $M$ in its comformal class, and all embedded FBMHs in $M$ are properly embedded, we show the existence of a sequence of properly embedded equidistributed FBMHs. This work extends the result of Ambrozio-Montezuma [2].

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Yucheng Tu. 2020-12-01. Locally Maximizing Metric of Width on Manifolds with Boundary. https://arxiv.org/abs/2008.04425

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