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:
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arXiv e-prints
- Pub Date:
- April 2022
- DOI:
- 10.48550/arXiv.2204.04923
- arXiv:
- arXiv:2204.04923
- Bibcode:
- 2022arXiv220404923C
- Keywords:
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- Mathematics - Analysis of PDEs