Parametric inequalities and Weyl law for the volume spectrum
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918002473041920 |
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| author | Guth, Larry Liokumovich, Yevgeny |
| author_facet | Guth, Larry Liokumovich, Yevgeny |
| contents | We show that the Weyl law for the volume spectrum in a compact Riemannian manifold conjectured by Gromov can be derived from parametric generalizations of two famous inequalities: isoperimetric inequality and coarea inequality. We prove two such generalizations in low dimensions and obtain the Weyl law for 1-cycles in 3-manifolds. We also give a new proof of the Almgren isomorphism theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_11805 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Parametric inequalities and Weyl law for the volume spectrum Guth, Larry Liokumovich, Yevgeny Differential Geometry Geometric Topology Spectral Theory 35P20, 53A10 We show that the Weyl law for the volume spectrum in a compact Riemannian manifold conjectured by Gromov can be derived from parametric generalizations of two famous inequalities: isoperimetric inequality and coarea inequality. We prove two such generalizations in low dimensions and obtain the Weyl law for 1-cycles in 3-manifolds. We also give a new proof of the Almgren isomorphism theorem. |
| title | Parametric inequalities and Weyl law for the volume spectrum |
| topic | Differential Geometry Geometric Topology Spectral Theory 35P20, 53A10 |
| url | https://arxiv.org/abs/2202.11805 |