A stochastic representation for mean curvature type geometric flows

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

A smooth solution { (t)}t∈[0,T ] ⊂ Rd 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 Xν x(t) ∈ T for...

A representation for some groups, a geometric approach

‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎ ‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎, ‎to establish a representation for some groups on $R^{n} (ngeq 1)$‎. ‎Among other things‎, ‎we investigate the surjectivity and faithfulness of the representation‎. At the end‎, ‎we give some app...

Algorithms for stochastic approximations of curvature flows

Curvature flows have been extensively considered from a deterministic point of view. They have been shown to be useful for a number of applications including crystal growth, flame propagation, and computer vision. In some previous work [1], we have described a random particle system, evolving on the discretized unit circle, whose profile converges toward the Gauss-Minkowsky transformation of so...

A Priori Estimates for Lagrangian Mean Curvature Flows

A FEM for Mean Curvature and Related Flows

Figure 4. Singularity formation when boundary conditions are such that the catenoid solution does not exist. 7 Figure 3. Limiting catenoid surface obtained from an initially cylindrical surface. is the minimal surface with the same xed boundary. Figure 3 shows the required catenoid. This surface was obtained as the limiting surface of a FEM evolution starting from a cylindrical initial surface ...