A Note on Alexandrov Immersed Mean Curvature Flow
The Journal of Geometric Analysis(2024)
摘要
We demonstrate that the property of being Alexandrov immersed is preserved along mean curvature flow. Furthermore, we demonstrate that mean curvature flow techniques for mean convex embedded flows such as noncollapsing and gradient estimates also hold in this setting. We also indicate the necessary modifications to the work of Brendle–Huisken to allow for mean curvature flow with surgery in the Alexandrov immersed, 2-dimensional setting.
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关键词
Mean curvature flow,Noncollapsing estimates,Alexandrov immersions,53E10,53C42,53C21
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