Dimension Bound of Singular Set of One-Phase Free Boundary Problems in Spaces with Two-Sided Ricci Bound
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908965067030528 |
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| author | Wang, Kai-Hsiang |
| author_facet | Wang, Kai-Hsiang |
| contents | In this article, we show that for one-phase free boundary problems in noncollapsed limits of $n$-dimensional manifolds with two-sided Ricci curvature bounds, the Hausdorff dimension of the singular set of the free boundary can be bounded by $n-5$, which is sharp in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13324 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dimension Bound of Singular Set of One-Phase Free Boundary Problems in Spaces with Two-Sided Ricci Bound Wang, Kai-Hsiang Analysis of PDEs Differential Geometry 53C23, 49Q10, 58J90 In this article, we show that for one-phase free boundary problems in noncollapsed limits of $n$-dimensional manifolds with two-sided Ricci curvature bounds, the Hausdorff dimension of the singular set of the free boundary can be bounded by $n-5$, which is sharp in this context. |
| title | Dimension Bound of Singular Set of One-Phase Free Boundary Problems in Spaces with Two-Sided Ricci Bound |
| topic | Analysis of PDEs Differential Geometry 53C23, 49Q10, 58J90 |
| url | https://arxiv.org/abs/2604.13324 |