A Stochastic Representation for Mean Curvature Type Geometric Flows by H. Mete Soner

Dynamic Programming for Stochastic Target Problems and Geometric Flows

Given a controlled stochastic process, the reachability set is the collection of all initial data from which the state process can be driven into a target set at a specified time. Differential properties of these sets are studied by the dynamic programming principle which is proved by the Jankov-von Neumann measurable selection theorem. This principle implies that the reachability sets satisfy ...

Singularities and uniqueness of cylindrically symmetric surfaces moving by mean curvature

Flow by mean curvature of surfaces of any codimension

Convergence of the Phase-Field Equations to the Mullins-Sekerka Problem with Kinetic Undercooling

I prove that the solutions of the phase-field equations, on a subsequence, converge to a weak solution of the Mullins-Sekerka problem with kinetic undercooling. The method is based on energy estimates, a monotonicity formula, and the equipartition of the energy at each time. I also show that for almost all t, the limiting interface is ( d 1)-rectifiable with a square-integrable mean-curvature v...

Martingale Representation Theorem for the G-expectation

This paper considers the nonlinear theory of G-martingales as introduced by Peng in [16, 17]. A martingale representation theorem for this theory is proved by using the techniques and the results established in [20] for the second order stochastic target problems and the second order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a ...