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arXiv · 2304.02722

Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies

Lorenzo Sarnataro·Douglas Stryker
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Abstract

We prove the optimal $C^{1,1}$ regularity for minimizers of the prescribed mean curvature functional over isotopy classes. As an application, we find an embedded sphere of prescribed mean curvature in the round 3-sphere for an open dense set of prescribing functions with $L^{\infty}$ norm at most 0.547.

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Lorenzo Sarnataro, Douglas Stryker. 2023-04-05. Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies. https://arxiv.org/abs/2304.02722

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