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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.03912 |
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Table of Contents:
- We prove that the volume preserving fractional mean curvature flow starting from a convex set does not develop singularities along the flow. By the recent result of Cesaroni-Novaga \cite{CN} this then implies that the flow converges to a ball exponentially fast. In the proof we show that the apriori estimates due to Cinti-Sinestrari-Valdinoci \cite{CSV2} imply the $C^{1+α}$-regularity of the flow and then provide a regularity argument which improves this into $C^{2+α}$-regularity of the flow. The regularity step from $C^{1+α}$ into $C^{2+α}$ does not rely on convexity and can probably be adopted to more general setting.