Non-uniqueness of curve shortening flow
Differential Geometry
2022-05-10 v1 Analysis of PDEs
Abstract
We formulate a uniqueness conjecture for curve shortening flow of proper curves on certain symmetric surfaces and give an example of a non-flat metric on the plane with respect to which curve shortening flow is not unique. That is, with respect to a suitably chosen metric, we construct a non-static solution to curve shortening flow starting from a properly embedded geodesic.
Cite
@article{arxiv.2205.03442,
title = {Non-uniqueness of curve shortening flow},
author = {Luke Thomas Peachey},
journal= {arXiv preprint arXiv:2205.03442},
year = {2022}
}