Mean curvature flows with prescribed singular sets
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917410956640256 |
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| author | Tsiamis, Raphael |
| author_facet | Tsiamis, Raphael |
| contents | For every closed set $K \subset \mathbb{R}^n$ and every $m \geq 2$, we construct a mean-convex ancient solution to mean curvature flow of hypersurfaces in $\mathbb{R}^{m+n}$, with respect to a smooth Riemannian metric arbitrarily $C^\infty$-close to the Euclidean metric, whose first-time singular set is exactly $K \times \{0\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14139 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mean curvature flows with prescribed singular sets Tsiamis, Raphael Differential Geometry Analysis of PDEs For every closed set $K \subset \mathbb{R}^n$ and every $m \geq 2$, we construct a mean-convex ancient solution to mean curvature flow of hypersurfaces in $\mathbb{R}^{m+n}$, with respect to a smooth Riemannian metric arbitrarily $C^\infty$-close to the Euclidean metric, whose first-time singular set is exactly $K \times \{0\}$. |
| title | Mean curvature flows with prescribed singular sets |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2604.14139 |