Department of Mathematics2024-11-0920030091-179810.1214/aop/10554257732-s2.0-78649704657https://hdl.handle.net/20.500.14288/4057A smooth solution {Gamma(t)}(tis an element of[0,T]) subset of R-d of a parabolic geometric flow is characterized as the reachability set of a stochastic target problem. In this control problem the controller tries to steer the state process into a given deterministic set T with probability one. The reachability set, V(t), for the target problem is the set of all initial data x from which the state process X-X(v)(t) is an element of T for some control process v. This representation is proved by studying the squared distance function to Gamma(t). For the codimension k mean curvature flow, the state process is dX(t) = root2P dW(t), where W(t) is a d-dimensional Brownian motion, and the control P is any projection matrix onto a (d - k)-dimensional plane. Smooth solutions of the inverse mean curvature flow and a discussion of non smooth solutions are also given.pdfMathematicsStatistics and probabilityJournal Articlehttps://doi.org/10.1214/aop/1055425773284592200011Q1NOIR00464