Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Novaga

Stability of the ball under volume preserving fractional mean curvature flow

created by cesaroni on 11 Apr 2022
modified by novaga on 04 Apr 2024


Published Paper

Inserted: 11 apr 2022
Last Updated: 4 apr 2024

Journal: Adv. Calc. Var.
Volume: 17
Number: 2
Pages: 503-520
Year: 2024

ArXiv: 2204.04923 PDF


We consider the volume constrained fractional mean curvature flow of a nearly spherical set, and prove long time existence and asymptotic convergence to a ball. The result applies in particular to convex initial data, under the assumption of global existence. Similarly, we show exponential convergence to a constant for the fractional mean curvature flow of a periodic graph.