Flat flows of periodic Lipschitz subgraphs for generalized nonlocal perimeters
Abstract
We prove the existence and the $\tfrac12$-Hölder continuity in time of flat flows for periodic Lipschitz subgraphs, whose evolution is governed by the gradient flow of generalized nonlocal perimeters. Moreover, we show that the flat flow satisfies the semigroup property and, as a consequence, the generalized perimeter decreases along the evolution. Finally, we prove that halfspaces are global minimizers of the generalized nonlocal perimeters and act as attractors for the dynamics. Our theory covers several generalized perimeters, including fractional and Riesz-type perimeters (defined on entire periodic subgraphs through suitable renormalization procedures) and the Minkowski pre-content.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Mathematical Dynamics and Fractals
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Communications in Analysis and Geometry
- Volume
- 34
- Issue
- 3
- Pages
- 845–889
- Publication date
- 1 January 2026
- Language
- EN