Convergence of the volume preserving fractional mean curvature flow for convex sets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913707814027264 |
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| author | Julin, Vesa La Manna, Domenico Angelo |
| author_facet | Julin, Vesa La Manna, Domenico Angelo |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03912 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence of the volume preserving fractional mean curvature flow for convex sets Julin, Vesa La Manna, Domenico Angelo Analysis of PDEs 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. |
| title | Convergence of the volume preserving fractional mean curvature flow for convex sets |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2307.03912 |