A stochastic target approach to Ricci flow on surfaces

DOI10.1214/15-AOP1003zbMath1342.60107arXiv1209.4150OpenAlexW1836323122MaRDI QIDQ282517

Robert W. Neel, Ionel Popescu

Publication date: 12 May 2016

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.4150

zbMATH Keywords

Brownian motionRicci flowcouplingstochastic target problem

Mathematics Subject Classification ID

Related Items (2)

Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates ⋮ An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions

Cites Work

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• Coupling of Brownian motions and Perelman's \(\mathcal L\)-functional
• Brownian motion with respect to time-changing Riemannian metrics, applications to Ricci flow
• Monotonicity properties of the Neumann heat kernel in the ball
• Non-explosion of diffusion processes on manifolds with time-dependent metric
• Mirror coupling of reflecting Brownian motion and an application to Chavel's conjecture
• A probabilistic numerical method for fully nonlinear parabolic PDEs
• Convergence of time-inhomogeneous geodesic random walks and its application to coupling methods
• Brownian motion with killing and reflection and the ``hot-spots problem
• Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
• Efficient Markovian couplings: Examples and counterexamples
• Shy couplings
• Shy and fixed-distance couplings of Brownian motions on manifolds
• Noncoalescence for the Skorohod equation in a convex domain of \({\mathbb{R}}^ 2\)
• Brownian motion with respect to a metric depending on time; definition, existence and applications to Ricci flow
• Brownian couplings, convexity, and shyness
• Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds
• Coupling of multidimensional diffusions by reflection
• Gradient estimates on manifolds using coupling
• On the ``hot spots conjecture of J. Rauch
• A survey and some generalizations of Bessel processes
• A stochastic representation for mean curvature type geometric flows
• On the noncoalescence of a two point Brownian motion reflecting on a circle
• Coupled Brownian motions and partial domain monotonicity for the Neumann heat kernel
• Shy couplings, \(\mathrm{CAT}(0)\) spaces, and the lion and man
• Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below
• Horizontal Diffusion in C 1 Path Space
• Scaling coupling of reflecting Brownian motions and the hot spots problem
• Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
• Stochastic Differential Geometry, a Coupling Property, and Harmonic Maps
• Nonnegative ricci curvature and the brownian coupling property
• A Probabilistic Approach to Gradient Estimates
• A STOCHASTIC REPRESENTATION FOR THE LEVEL SET EQUATIONS

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