https://neckpinch.com/authors/dmitry-vorotnikov/New arXiv papers by Dmitry Vorotnikov, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1711.03864/arxiv:1711.03864Fri, 10 Nov 2017 00:00:00 GMTWenhui Shi, Dmitry Vorotnikov — 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.Mean curvature flowStability & uniqueness