Mean curvature flow through singularities
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911188612284416 |
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| author | Haslhofer, Robert |
| author_facet | Haslhofer, Robert |
| contents | We first give a general introduction to the mean curvature flow, and then discuss fundamental results established over the last 10 years that yield a precise theory for the flow through singularities in $\mathbb{R}^3$. With the aim of developing a satisfying theory in higher dimensions, we then describe our recent classification of all noncollapsed singularities in $\mathbb{R}^4$. Finally, we provide a detailed discussion of open problems and conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01355 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean curvature flow through singularities Haslhofer, Robert Differential Geometry Analysis of PDEs We first give a general introduction to the mean curvature flow, and then discuss fundamental results established over the last 10 years that yield a precise theory for the flow through singularities in $\mathbb{R}^3$. With the aim of developing a satisfying theory in higher dimensions, we then describe our recent classification of all noncollapsed singularities in $\mathbb{R}^4$. Finally, we provide a detailed discussion of open problems and conjectures. |
| title | Mean curvature flow through singularities |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2510.01355 |