Open Access
2006 Global geometry under isotropic Brownian flows
Sreekar Vadlamani, Robert Adler
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Electron. Commun. Probab. 11: 182-192 (2006). DOI: 10.1214/ECP.v11-1212


We consider global 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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Sreekar Vadlamani. Robert Adler. "Global geometry under isotropic Brownian flows." Electron. Commun. Probab. 11 182 - 192, 2006.


Accepted: 7 September 2006; Published: 2006
First available in Project Euclid: 4 June 2016

zbMATH: 1110.60064
MathSciNet: MR2266708
Digital Object Identifier: 10.1214/ECP.v11-1212

Primary: Primary 60H10
Secondary: 28A75 , 60J60 , Secondary 52A39

Keywords: Brownian flows , evolution equations , Lipschitz-Killing curvatures , Lyapunov exponents , Manifolds , Stochastic flows

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