Collapse of the mean curvature flow for certain kind of invariant hypersurfaces in a Hilbert space

Naoyuki Koike

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arXiv · 1607.02899

Collapse of the mean curvature flow for certain kind of invariant hypersurfaces in a Hilbert space

Naoyuki Koike

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Abstract

In this paper, we investigate the regularized mean curvature flow starting from an invariant hypersurface in a Hilbert space equipped with an isometric and almost free action of a Hilbert Lie group whose orbits are regularized minimal. We prove that, if the invariant hypersurface satisfies a certain kind of horizontally convexity condition, then it collapses to an orbit of the Hilbert Lie group action along the regularized mean curvature flow.

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Naoyuki Koike. 2016-07-11. Collapse of the mean curvature flow for certain kind of invariant hypersurfaces in a Hilbert space. https://arxiv.org/abs/1607.02899

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