Integral type Gauss-Green formula on non-collapsed RCD spaces and its applications
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914620790276096 |
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| author | Huang, Zhangkai |
| author_facet | Huang, Zhangkai |
| contents | We prove an integral type Gauss-Green formula on non-collapsed RCD spaces using the strong locality of the Laplacian and an eigenfunction approximation method. As applications, we generalize Colding's monotonicity formulas and prove an asymptotic formula linking the mean curvature of a hypersurface at a given point to the volume of small balls centered at that point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01108 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integral type Gauss-Green formula on non-collapsed RCD spaces and its applications Huang, Zhangkai Differential Geometry Metric Geometry 26B20, 26B30, 53C23 We prove an integral type Gauss-Green formula on non-collapsed RCD spaces using the strong locality of the Laplacian and an eigenfunction approximation method. As applications, we generalize Colding's monotonicity formulas and prove an asymptotic formula linking the mean curvature of a hypersurface at a given point to the volume of small balls centered at that point. |
| title | Integral type Gauss-Green formula on non-collapsed RCD spaces and its applications |
| topic | Differential Geometry Metric Geometry 26B20, 26B30, 53C23 |
| url | https://arxiv.org/abs/2606.01108 |