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arXiv · 2307.01828

Free boundary minimal disks in convex balls

Robert Haslhofer·Daniel Ketover
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Abstract

In this paper, we prove that every strictly convex 3-ball with nonnegative Ricci-curvature contains at least 3 embedded free-boundary minimal 2-disks for any generic metric, and at least 2 solutions even without genericity assumption. Our approach combines ideas from mean curvature flow, min-max theory and degree theory. We also establish the existence of smooth free-boundary mean-convex foliations. In stark contrast to our prior work in the closed setting, the present result is sharp for generic metrics.

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Robert Haslhofer, Daniel Ketover. 2023-07-04. Free boundary minimal disks in convex balls. https://arxiv.org/abs/2307.01828

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