A stochastic representation for mean curvature type geometric flows

DOI10.1214/aop/1055425773zbMath1080.60076OpenAlexW2013316975MaRDI QIDQ1431481

Halil Mete Soner, Nizar Touzi

Publication date: 10 June 2004

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

Full work available at URL: https://projecteuclid.org/euclid.aop/1055425773

zbMATH Keywords

mean curvature flowinverse mean curvature flowstochastic target problem

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Dynamic programming in optimal control and differential games (49L20) Nonlinear parabolic equations (35K55) Variational problems in a geometric measure-theoretic setting (49Q20) Diffusion processes (60J60)

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Cites Work

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• Flow by mean curvature of convex surfaces into spheres
• Motion of level sets by mean curvature. I
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• A short note on the evolution of a surface by its mean curvature
• Level set approach to mean curvature flow in arbitrary codimension
• Curvature and distance function from a manifold
• Motion of a set by the curvature of its boundary
• Forward-backward stochastic differential equations and their applications
• Backward stochastic differential equations with constraints on the gains-process
• Dynamic programming for stochastic target problems and geometric flows
• A Representation Formula for the Mean Curvature Motion
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Superreplication Under Gamma Constraints
• Front Propagation and Phase Field Theory
• A STOCHASTIC REPRESENTATION FOR THE LEVEL SET EQUATIONS
• Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations