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Chenn, Ilias; Fournodavlos, G.; Sigal, I. M.

The effective dynamics of the volume preserving mean curvature flow. (English) Zbl 1396.82014

J. Stat. Phys. 172, No. 2, 458-476 (2018).
Summary: We consider the dynamics of small closed submanifolds (‘bubbles’) under the volume preserving mean curvature flow. We construct a map from \((n+1)\)-dimensional Euclidean space into a given \((n+1)\)-dimensional Riemannian manifold which characterizes the existence, stability and dynamics of constant mean curvature submanifolds. This is done in terms of a reduced area function on the Euclidean space, which is given constructively and can be computed perturbatively. This allows us to derive adiabatic and effective dynamics of the bubbles. The results can be mapped by rescaling to the dynamics of fixed size bubbles in almost Euclidean Riemannian manifolds.

Cited in 2 Documents

MSC:

82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
82C27 Dynamic critical phenomena in statistical mechanics
82C28 Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics
53C40 Global submanifolds

Keywords:

volume preserving mean curvature flow; constant mean curvature surface; submanifold; mean curvature flow; adiabatic dynamic; effective dynamic
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References:

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