Stability of the ball under volume preserving fractional mean curvature flow
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 arXiv:
 arXiv:2204.04923
 Bibcode:
 2022arXiv220404923C
 Keywords:

 Mathematics  Analysis of PDEs