Uniformly compressing mean curvature flow
Analysis of PDEs
2018-09-18 v2
Abstract
Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a related geometric flow which is free of these drawbacks. Our flow can be viewed as a formal gradient flow on a certain submanifold of the Wasserstein space of probability measures endowed with Otto's Riemannian structure. We obtain a number of analytic results concerning well-posedness and long-time stability which are however restricted to the 1D case of evolution of loops.
Cite
@article{arxiv.1711.03864,
title = {Uniformly compressing mean curvature flow},
author = {Wenhui Shi and Dmitry Vorotnikov},
journal= {arXiv preprint arXiv:1711.03864},
year = {2018}
}