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Minkowski inequality
on complete Riemannian manifolds with nonnegative Ricci
curvature
Luca Benatti, Mattia Fogagnolo and Lorenzo Mazzieri |
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Vol. 17 (2024), No. 9, 3039–3077
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Abstract |
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We consider Riemannian manifolds of dimension at least , 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 -capacitary potentials in -nonparabolic manifolds with nonnegative Ricci curvature. |
Keywords
geometric inequalities, nonlinear potential theory,
monotonicity formulas, inverse mean curvature flow
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Mathematical Subject Classification
Primary: 35A16, 35B06, 31C15, 53C21, 53E10
Secondary: 49Q10, 39B62
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Milestones
Received: 18 March 2022
Revised: 18 May 2023
Accepted: 18 July 2023
Published: 1 November 2024
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Authors |
| Luca Benatti | |
| Università di Pisa Pisa Italy |
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| Mattia Fogagnolo | |
| Università di Padova Padova Italy |
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| Lorenzo Mazzieri | |
| Università degli Studi di
Trento Povo Italy |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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