A semigroup approach to Finsler geometry: Bakry-Ledoux's isoperimetric inequality
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2016
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| _version_ | 1866910596110221312 |
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| author | Ohta, Shin-ichi |
| author_facet | Ohta, Shin-ichi |
| contents | We develop the celebrated semigroup approach à la Bakry et al on Finsler manifolds, where natural Laplacian and heat semigroup are nonlinear, based on the Bochner-Weitzenböck formula established by Sturm and the author. We show the $L^1$-gradient estimate on Finsler manifolds (under some additional assumptions in the noncompact case), which is equivalent to a lower weighted Ricci curvature bound and the improved Bochner inequality. As a geometric application, we prove Bakry-Ledoux's Gaussian isoperimetric inequality, again under some additional assumptions in the noncompact case. This extends Cavalletti-Mondino's inequality on reversible Finsler manifolds to non-reversible metrics, and improves the author's previous estimate, both based on the localization (also called needle decomposition) method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1602_00390 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | A semigroup approach to Finsler geometry: Bakry-Ledoux's isoperimetric inequality Ohta, Shin-ichi Differential Geometry Analysis of PDEs Metric Geometry We develop the celebrated semigroup approach à la Bakry et al on Finsler manifolds, where natural Laplacian and heat semigroup are nonlinear, based on the Bochner-Weitzenböck formula established by Sturm and the author. We show the $L^1$-gradient estimate on Finsler manifolds (under some additional assumptions in the noncompact case), which is equivalent to a lower weighted Ricci curvature bound and the improved Bochner inequality. As a geometric application, we prove Bakry-Ledoux's Gaussian isoperimetric inequality, again under some additional assumptions in the noncompact case. This extends Cavalletti-Mondino's inequality on reversible Finsler manifolds to non-reversible metrics, and improves the author's previous estimate, both based on the localization (also called needle decomposition) method. |
| title | A semigroup approach to Finsler geometry: Bakry-Ledoux's isoperimetric inequality |
| topic | Differential Geometry Analysis of PDEs Metric Geometry |
| url | https://arxiv.org/abs/1602.00390 |