The Regularized Mean Curvature Flow for Invariant Hypersurfaces in a Hilbert Space

  • Naoyuki Koike
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


In this note, I state some results for the regularized mean curvature flow starting from invariant hypersurfaces in a Hilbert space equipped with an isometric almost free Hilbert Lie group action whose orbits are minimal regularizable submanifolds. First we derive the evolution equations for some geometric quantities along this flow. Some of the evolution equations are described by using the O’Neill fundamental tensor of the orbit map of the Hilbert Lie group action, where we note that the O’Neill fundamental tensor implies the obstruction for the integrability of the horizontal distribution of the orbit map. Next, by using the evolution equations, we derive some results for this flow. Furthermore, we derive some results for the mean curvature flow starting from compact Riemannian suborbifolds in the orbit space (which is a Riemannian orbifold) of the Hilbert Lie group action.


Curvature Flow Curvature Vector Riemannian Connection Fundamental Tensor Hilbert Space Versus 
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The author is grateful to JSPS for support (Grant-in-Aid for Science Research (C), no.25400076).


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of Mathematics Faculty of ScienceTokyo University of ScienceShinjuku-kuJapan

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