Convergence of curve shortening flow to translating soliton

Curve Shortening Flow in a Riemannian Manifold

In this paper, we systemally study the long time behavior of the curve shortening flow in a closed or non-compact complete locally Riemannian symmetric manifold. Assume that we have a global flow. Then we can exhibit a a limit for the global behavior of the flow. In particular, we show the following results. 1). Let M be a compact locally symmetric space. If the curve shortening flow exists for...

An Introduction to Curve-Shortening and the Ricci Flow

Results of Triangles Under Discrete Curve Shortening Flow

In this paper, we analyze the results of triangles under discrete curve shortening flow, specifically isosceles triangles with top angles greater than π3 , and scalene triangles. By considering the location of the three vertices of the triangle after some small time , we use the definition of the derivative to calculate a system of differential equations involving parameters that can describe t...

Ergodicity of Stochastic Curve Shortening Flow in the Plane

We study models of the motion by mean curvature of an (1+1) dimensional interface with random forcing. For the well-posedness of the models we prove existence and uniqueness for certain degenerate nonlinear stochastic evolution equations in the variational framework of Krylov-Rozovskĭı, replacing the standard coercivity assumption by a Lyapunov type condition. Ergodicity is established for the ...

Grid peeling and the affine curve-shortening flow

In this paper we study an experimentally-observed connection between two seemingly unrelated processes, one from computational geometry and the other from differential geometry. The first one (which we call grid peeling) is the convex-layer decomposition of subsets G ⊂ Z of the integer grid, previously studied for the particular case G = {1, . . . ,m} by Har-Peled and Lidický (2013). The second...