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Singularities of Mean Curvature Flow with Bounded Total Curvature
Abstract
We prove that every tangent flow at the first singular time of a smooth, closed, embedded mean curvature flow has smooth support, provided that the total curvature satisfies supt∈[0,T)∫Mt|A|n dμt<∞. This extends Ilmanen's smoothness result for tangent flows to higher dimensions.
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BibTeX
@misc{han2026singularities,
title = {{Singularities of Mean Curvature Flow with Bounded Total Curvature}},
author = {Yongheng Han and Zhen Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18197},
eprint = {2610.18197},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18197},
}
RIS
TY - UNPB
TI - Singularities of Mean Curvature Flow with Bounded Total Curvature
AU - Yongheng Han
AU - Zhen Wang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18197
UR - https://arxiv.org/abs/2610.18197
AB - We prove that every tangent flow at the first singular time of a smooth, closed, embedded mean curvature flow has smooth support, provided that the total curvature satisfies sup_t∈[0,T)∫_M_t|A|^n dμ_t<∞. This extends Ilmanen's smoothness result for tangent flows to higher dimensions.
ER -