Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916273410015232 |
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| author | Manini, Davide |
| author_facet | Manini, Davide |
| contents | We prove a sharp isoperimetric inequality for measured Finsler manifolds having non-negative Ricci curvature and Euclidean volume growth. We also prove a rigidity result for this inequality, under the additional hypotheses of boundedness of the isoperimetric set and the finite reversibility of the space.
As a consequence, we deduce the rigidity of the weighted anisotropic isoperimetric inequality for cones in the Euclidean space, in the irreversible setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_05130 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature Manini, Davide Differential Geometry Metric Geometry 58B20 (Primary) 51Fxx (Secondary) We prove a sharp isoperimetric inequality for measured Finsler manifolds having non-negative Ricci curvature and Euclidean volume growth. We also prove a rigidity result for this inequality, under the additional hypotheses of boundedness of the isoperimetric set and the finite reversibility of the space. As a consequence, we deduce the rigidity of the weighted anisotropic isoperimetric inequality for cones in the Euclidean space, in the irreversible setting. |
| title | Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature |
| topic | Differential Geometry Metric Geometry 58B20 (Primary) 51Fxx (Secondary) |
| url | https://arxiv.org/abs/2212.05130 |