The Effective Dynamics of the Volume Preserving Mean Curvature Flow
| Autor: | Israel Michael Sigal, Grigorios Fournodavlos, Ilias Chenn |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
Mean curvature flow Mean curvature 010308 nuclear & particles physics Euclidean space 010102 general mathematics Mathematical analysis Statistical and Nonlinear Physics Function (mathematics) Riemannian manifold Submanifold 01 natural sciences 0103 physical sciences Euclidean geometry Constant-mean-curvature surface Mathematics::Differential Geometry 0101 mathematics Mathematical Physics |
| Zdroj: | Journal of Statistical Physics. 172:458-476 |
| ISSN: | 1572-9613 0022-4715 |
| DOI: | 10.1007/s10955-018-2041-x |
| Popis: | We consider the dynamics of small closed submanifolds (‘bubbles’) under the volume preserving mean curvature flow. We construct a map from ( $$\text {n}+1$$ )-dimensional Euclidean space into a given ( $$\text {n}+1$$ )-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. |
| Databáze: | OpenAIRE |
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