Nonnegative Ricci Curvature and Uniformly Convex Boundary Forces Compactness
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914618210779136 |
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| author | Yan, Zetian Zhu, Xingyu |
| author_facet | Yan, Zetian Zhu, Xingyu |
| contents | We confirm a compactness conjecture of M. Li. If a complete Riemannian manifold has nonnegative Ricci curvature and uniformly convex boundary in the sense that the second fundamental form satisfies $h\ge1$. Then we prove it is compact, and consequently has finite fundamental group. The proof uses monotone quantities constructed via positive proper harmonic functions with Neumann condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31477 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonnegative Ricci Curvature and Uniformly Convex Boundary Forces Compactness Yan, Zetian Zhu, Xingyu Differential Geometry Metric Geometry 53C21, 53C24 We confirm a compactness conjecture of M. Li. If a complete Riemannian manifold has nonnegative Ricci curvature and uniformly convex boundary in the sense that the second fundamental form satisfies $h\ge1$. Then we prove it is compact, and consequently has finite fundamental group. The proof uses monotone quantities constructed via positive proper harmonic functions with Neumann condition. |
| title | Nonnegative Ricci Curvature and Uniformly Convex Boundary Forces Compactness |
| topic | Differential Geometry Metric Geometry 53C21, 53C24 |
| url | https://arxiv.org/abs/2605.31477 |