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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.12673 |
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| _version_ | 1866914622435491840 |
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| author | Lee, Man-Chun Lee, Tang-Kai |
| author_facet | Lee, Man-Chun Lee, Tang-Kai |
| contents | In this work, we establish a local smoothing result on metrics with small curvature concentration with respect to Sobolev constants and volume growth. In contrast with all previous works, we remove the Ricci curvature condition and completely localize the smoothing. As an application, we prove the compactness of the space of compact manifolds with bounded curvature concentration under Ahlfors $n$-regularity and bounded Sobolev constant. In the complete non-compact case, we show that manifolds with Euclidean type Sobolev inequality, Euclidean volume growth, and small curvature concentration are necessarily diffeomorphic to Euclidean spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local mollification of metrics with small curvature concentration Lee, Man-Chun Lee, Tang-Kai Differential Geometry In this work, we establish a local smoothing result on metrics with small curvature concentration with respect to Sobolev constants and volume growth. In contrast with all previous works, we remove the Ricci curvature condition and completely localize the smoothing. As an application, we prove the compactness of the space of compact manifolds with bounded curvature concentration under Ahlfors $n$-regularity and bounded Sobolev constant. In the complete non-compact case, we show that manifolds with Euclidean type Sobolev inequality, Euclidean volume growth, and small curvature concentration are necessarily diffeomorphic to Euclidean spaces. |
| title | Local mollification of metrics with small curvature concentration |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.12673 |