Brownian motion with respect to a metric depending on time; definition, existence and applications to Ricci flow
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Publication:935362
DOI10.1016/j.crma.2008.05.004zbMath1144.58019OpenAlexW2093928738MaRDI QIDQ935362
Marc Arnaudon, Anton Thalmaier, Koléhè A. Coulibaly-Pasquier
Publication date: 6 August 2008
Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)
Full work available at URL: http://orbilu.uni.lu/handle/10993/13602
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Cites Work
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- Unnamed Item
- Flow by mean curvature of convex surfaces into spheres
- Gradient estimates for positive harmonic functions by stochastic analysis
- Stochastic calculus in manifolds. With an appendix by P.A. Meyer
- Gradient estimates for harmonic functions on regular domains in Riemannian manifolds
- Formulae for the derivatives of heat semigroups
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