Proper solutions of the $1/H$-flow and the Green kernel of the $p$-Laplacian
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917184273383424 |
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| author | Benatti, Luca Mari, Luciano Rigoli, Marco Setti, Alberto G. Xu, Kai |
| author_facet | Benatti, Luca Mari, Luciano Rigoli, Marco Setti, Alberto G. Xu, Kai |
| contents | We show existence and optimal growth estimate for the weak inverse mean curvature flow issuing from a point, on manifolds with certain curvature and isoperimetric conditions. These theorems imply analogous ones for the flow issuing from relatively compact sets. Some of the results are obtained by proving new decay estimates for the Green kernel of the $p$-Laplacian which fix a gap in the literature. Additionally, we address the convergence of renormalized $p$-capacitary potentials to the inverse mean curvature flow with outer obstacle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14591 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proper solutions of the $1/H$-flow and the Green kernel of the $p$-Laplacian Benatti, Luca Mari, Luciano Rigoli, Marco Setti, Alberto G. Xu, Kai Analysis of PDEs Differential Geometry We show existence and optimal growth estimate for the weak inverse mean curvature flow issuing from a point, on manifolds with certain curvature and isoperimetric conditions. These theorems imply analogous ones for the flow issuing from relatively compact sets. Some of the results are obtained by proving new decay estimates for the Green kernel of the $p$-Laplacian which fix a gap in the literature. Additionally, we address the convergence of renormalized $p$-capacitary potentials to the inverse mean curvature flow with outer obstacle. |
| title | Proper solutions of the $1/H$-flow and the Green kernel of the $p$-Laplacian |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2512.14591 |