Eventual regularization of fractional mean curvature flow
Abstract
Abstract We show that any open set that is a finite distance away from a Lipschitz subgraph will become a Lipschitz subgraph after flowing under fractional mean curvature flow for a finite, universal time. Our proof is quantitative and inherently nonlocal, as the corresponding statement is false for classical mean curvature flow. This is the first regularizing effect proven for weak solutions to nonlocal curvature flow.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Geometry and complex manifolds
Publication details
- Journal / source
- Communications on Pure and Applied Mathematics
- Publisher
- Wiley
- Volume
- 79
- Issue
- 6
- Pages
- 1399–1448
- Publication date
- 12 January 2026
- Language
- EN