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arXiv · 2306.07714

Free boundary flow with surgery

Robert Haslhofer
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Abstract

In this paper, we prove the existence of mean curvature flow with surgery for mean-convex surfaces with free boundary. To do so, we implement our recent new approach for constructing flows with surgery without a prior estimates in the free boundary setting. The flow either becomes extinct in finite time or for $t\to\infty$ converges smoothly in the one or two sheeted sense to a finite collection of stable connected minimal surfaces with empty or free boundary (in particular, there are no surgeries for $t$ sufficiently large). Our free boundary flow with surgery will be applied in forthcoming work with Ketover, where we will address the existence problem for $3$ free boundary minimal disks in convex balls.

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Robert Haslhofer. 2023-06-13. Free boundary flow with surgery. https://doi.org/10.2140/gt.2026.30.1

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