Global geometry under isotropic Brownian flows

Details Global geometry under isotropic Brownian flows Global geometry under isotropic Brownian flows

2008-08-05

arxiv.org/abs/0808.0720v1

Electronic Communications in Probability, volume 11, 182--192. 2006

Mathematics

Probability

12 pages

Scientific paper

We consider global geometric properties of a codimension one manifold embedded in Euclidean space, as it evolves under an isotropic and volume preserving Brownian flow of diffeomorphisms. In particular, we obtain expressions describing the expected rate of growth of the Lipschitz-Killing curvatures, or intrinsic volumes, of the manifold under the flow. These results shed new light on some of the intriguing growth properties of flows from a global perspective, rather than the local perspective, on which there is a much larger literature.

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