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In this paper, we investigate a regularized mean curvature flow starting froman invariant hypersurface in a Hilbert space equipped with an isometric andalmost free action of a Hilbert Lie group whose orbits are minimalregularizable submanifolds. We prove that, if the initial invarianthypersurface satisfies a certain kind of horizontally convexity condition andsome additional conditions, then it collapses to an orbit of the Hilbert Liegroup action along the regularized mean curvature flow. In the final section,we state a vision for applying the study of the regularized mean curvature flowto the gauge theory.

Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory