# Stability of the ball under volume preserving fractional mean curvature flow

@inproceedings{Cesaroni2022StabilityOT, title={Stability of the ball under volume preserving fractional mean curvature flow}, author={Annalisa Cesaroni and Matteo Novaga}, year={2022} }

. 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.

## One Citation

### Asymptotic of the Discrete Volume-Preserving Fractional Mean Curvature Flow via a Nonlocal Quantitative Alexandrov Theorem

- Mathematics
- 2022

We characterize the long time behaviour of a discrete-in-time approximation of the volume preserving fractional mean curvature ﬂow. In particular, we prove that the discrete ﬂow starting from any…

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We characterize the long time behaviour of a discrete-in-time approximation of the volume preserving fractional mean curvature ﬂow. In particular, we prove that the discrete ﬂow starting from any…

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Abstract In this paper we analyze the Euler implicit scheme for the volume preserving mean curvature flow. We prove the exponential convergence of the scheme to a finite union of disjoint balls with…

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