Research profile

Dmitry Vorotnikov

Works on stability & uniqueness and mean curvature flow.

NP-RC-0829230000-0003-1547-2572

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Stability & uniquenessMean curvature flow

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  1. Wenhui Shi

    1 joint worklatest 2017

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Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.

2017

math.APWider flowsv2arXiv:1711.03864

Uniformly compressing mean curvature flow

Wenhui 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
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NP-RC-082923 is Dmitry Vorotnikov's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.

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