Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914348469846016 |
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| author | Antonelli, Gioacchino Fogagnolo, Mattia Nardulli, Stefano Pozzetta, Marco |
| author_facet | Antonelli, Gioacchino Fogagnolo, Mattia Nardulli, Stefano Pozzetta, Marco |
| contents | This paper deals with quasi-local isoperimetric versions of the positive mass theorem on $3$-manifolds endowed with continuous complete metrics having nonnegative scalar curvature in a suitable weak sense. As a corollary, we derive existence results for isoperimetric sets in such low regularity setting. Our main tool is a new local version of the weak inverse mean curvature flow enjoying $C^0$-stable quantitative estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature Antonelli, Gioacchino Fogagnolo, Mattia Nardulli, Stefano Pozzetta, Marco Differential Geometry Mathematical Physics Analysis of PDEs Metric Geometry This paper deals with quasi-local isoperimetric versions of the positive mass theorem on $3$-manifolds endowed with continuous complete metrics having nonnegative scalar curvature in a suitable weak sense. As a corollary, we derive existence results for isoperimetric sets in such low regularity setting. Our main tool is a new local version of the weak inverse mean curvature flow enjoying $C^0$-stable quantitative estimates. |
| title | Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature |
| topic | Differential Geometry Mathematical Physics Analysis of PDEs Metric Geometry |
| url | https://arxiv.org/abs/2403.15972 |