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arXiv · 1711.03864

Uniformly compressing mean curvature flow

Wenhui Shi·Dmitry Vorotnikov
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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.

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Wenhui Shi, Dmitry Vorotnikov. 2018-09-17. Uniformly compressing mean curvature flow. https://arxiv.org/abs/1711.03864

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