On the Existence and Uniqueness of Ancient Rescaled Mean Curvature Flows
Differential Geometry
2022-12-22 v1 Analysis of PDEs
Abstract
We show existence of ancient solutions to the rescaled mean curvature flow starting from a given asymptotically conical self-expander. These are examples of mean curvature flows coming out of cones that are not self-similar. We also show a strong uniqueness theorem when the cone is generic and use it to classify mean curvature flows coming out of generic cones of small entropy in low dimensions.
Keywords
Cite
@article{arxiv.2212.10798,
title = {On the Existence and Uniqueness of Ancient Rescaled Mean Curvature Flows},
author = {Letian Chen},
journal= {arXiv preprint arXiv:2212.10798},
year = {2022}
}
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31 pages