Free boundary flow with surgery
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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Point processes and geometric inequalities
Publication details
- Journal / source
- Geometry & Topology
- Volume
- 30
- Issue
- 1
- Pages
- 1–22
- Publication date
- 19 January 2026
- Language
- EN