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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2101.06063 |
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| _version_ | 1866913572089495552 |
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| author | Benatti, Luca Fogagnolo, Mattia Mazzieri, Lorenzo |
| author_facet | Benatti, Luca Fogagnolo, Mattia Mazzieri, Lorenzo |
| contents | In this paper we consider Riemannian manifolds of dimension at least $3$, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski Inequality. We also characterise the equality case, provided the domain is strictly outward minimising and strictly mean convex. Along with the proof, we establish in full generality sharp monotonicity formulas, holding along the level sets of $p$-capacitary potentials in $p$-nonparabolic manifolds with nonnegative Ricci curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_06063 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Minkowski Inequality on complete Riemannian manifolds with nonnegative Ricci curvature Benatti, Luca Fogagnolo, Mattia Mazzieri, Lorenzo Differential Geometry Analysis of PDEs 35A16, 35B06, 31C15, 53C21, 53E10, 49Q10, 39B62 In this paper we consider Riemannian manifolds of dimension at least $3$, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski Inequality. We also characterise the equality case, provided the domain is strictly outward minimising and strictly mean convex. Along with the proof, we establish in full generality sharp monotonicity formulas, holding along the level sets of $p$-capacitary potentials in $p$-nonparabolic manifolds with nonnegative Ricci curvature. |
| title | Minkowski Inequality on complete Riemannian manifolds with nonnegative Ricci curvature |
| topic | Differential Geometry Analysis of PDEs 35A16, 35B06, 31C15, 53C21, 53E10, 49Q10, 39B62 |
| url | https://arxiv.org/abs/2101.06063 |