Free boundary flow with surgery

Haslhofer, Robert

doi:10.2140/gt.2026.30.1

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Free boundary flow with surgery

Robert Haslhofer

Geometry & Topology 30 (2026) 1–22

DOI: 10.2140/gt.2026.30.1

Abstract

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 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.

Keywords

mean curvature flow, flow with surgery, free boundary

Mathematical Subject Classification

Primary: 53E10

References

Publication

Received: 12 September 2023

Revised: 1 May 2025

Accepted: 22 August 2025

Published: 19 January 2026

Proposed: Bruce Kleiner

Seconded: Aaron Naber, David Fisher

Authors

Robert Haslhofer
Department of Mathematics University of Toronto Toronto, ON Canada

This article is currently available only to readers at paying institutions. If enough institutions subscribe to this Subscribe to Open journal for 2026, the article will become Open Access in early 2026. Otherwise, this article (and all 2026 articles) will be available only to paid subscribers.

Volume 30, issue 1 (2026)