ABP estimate on metric measure spaces via optimal transport
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929465997656064 |
|---|---|
| author | Han, Bang-Xian |
| author_facet | Han, Bang-Xian |
| contents | By using optimal transport theory, we establish a sharp Alexandroff--Bakelman--Pucci (ABP) type estimate on metric measure spaces with synthetic Riemannian Ricci curvature lower bounds, and prove some geometric and functional inequalities including a functional ABP estimate. Our result not only extends the border of ABP estimate, but also provides an effective substitution of Jacobi fields computation in the non-smooth framework, which has potential applications to many problems in non-smooth geometric analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | ABP estimate on metric measure spaces via optimal transport Han, Bang-Xian Metric Geometry Analysis of PDEs Differential Geometry Functional Analysis By using optimal transport theory, we establish a sharp Alexandroff--Bakelman--Pucci (ABP) type estimate on metric measure spaces with synthetic Riemannian Ricci curvature lower bounds, and prove some geometric and functional inequalities including a functional ABP estimate. Our result not only extends the border of ABP estimate, but also provides an effective substitution of Jacobi fields computation in the non-smooth framework, which has potential applications to many problems in non-smooth geometric analysis. |
| title | ABP estimate on metric measure spaces via optimal transport |
| topic | Metric Geometry Analysis of PDEs Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2408.10725 |