How close is too close for singular mean curvature flows?
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910875972009984 |
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| author | Daniels-Holgate, Joshua Hershkovits, Or |
| author_facet | Daniels-Holgate, Joshua Hershkovits, Or |
| contents | Suppose $(M^i_t)_{t\in [0,T)}$, $i=1,2$, are two mean curvature flows in $\mathbb{R}^{n+1}$ encountering a multiplicity one compact singularity at time $T$, in such a manner that for every $k$, the Hausdorff distance between the two flows, $d_H$, satisfies $d_{H}(M^1_t,M^2_t)/(T-t)^k \rightarrow 0$. We demonstrate that $M^1_t=M^2_t$ for every $t$. This generalizes a result of Martin-Hagemayer and Sesum, who proved the case where $M^1_t$ is itself a self-similarly shrinking flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How close is too close for singular mean curvature flows? Daniels-Holgate, Joshua Hershkovits, Or Differential Geometry Analysis of PDEs Suppose $(M^i_t)_{t\in [0,T)}$, $i=1,2$, are two mean curvature flows in $\mathbb{R}^{n+1}$ encountering a multiplicity one compact singularity at time $T$, in such a manner that for every $k$, the Hausdorff distance between the two flows, $d_H$, satisfies $d_{H}(M^1_t,M^2_t)/(T-t)^k \rightarrow 0$. We demonstrate that $M^1_t=M^2_t$ for every $t$. This generalizes a result of Martin-Hagemayer and Sesum, who proved the case where $M^1_t$ is itself a self-similarly shrinking flow. |
| title | How close is too close for singular mean curvature flows? |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2503.11522 |