Non-explosion of diffusion processes on manifolds with time-dependent metric

DOI10.1007/s00209-010-0704-7zbMath1226.53039arXiv0910.1730OpenAlexW2085625593MaRDI QIDQ636780

Robert Philipowski, Kazumasa Kuwada

Publication date: 30 August 2011

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.1730

zbMATH Keywords

diffusion processRicci flownon-explosionradial process

Mathematics Subject Classification ID

Related Items (17)

Diffusion semigroup on manifolds with time-dependent metrics ⋮ A stochastic target approach to Ricci flow on surfaces ⋮ A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric ⋮ Martingales on manifolds with time-dependent connection ⋮ Reflecting diffusion processes on manifolds carrying geometric flow ⋮ Spectral gap on Riemannian path space over static and evolving manifolds ⋮ Heat equation in vector bundles with time-dependent metric ⋮ Heat Kernel Coupled with Geometric Flow and Ricci Flow ⋮ A probabilistic approach for gradient estimates on time-inhomogeneous manifolds ⋮ The radial part of Brownian motion with respect to \(\mathcal L\)-distance under Ricci flow ⋮ Evolution systems of measures and semigroup properties on evolving manifolds ⋮ A coupling of Brownian motions in the \(\mathcal{L}_0\)-geometry ⋮ Convergence of time-inhomogeneous geodesic random walks and its application to coupling methods ⋮ Coupling of Brownian motions and Perelman's \(\mathcal L\)-functional ⋮ An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions ⋮ An isometric embedding of the g(t)-Brownian motion with application in stability and homotopy group ⋮ A probabilistic method for gradient estimates of some geometric flows

Cites Work

• Optimal transport and Perelman's reduced volume
• Brownian motion with respect to a metric depending on time; definition, existence and applications to Ricci flow
• The radial part of Brownian motion on a manifold: A semimartingale property
• The fundamental solution on manifolds with time-dependent metrics
• Horizontal Diffusion in C 1 Path Space
• ℒ-optimal transportation for Ricci flow
• Ricci flow, entropy and optimal transportation
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
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