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Self-similar solutions to the curve shortening flow
We give a classification of all self-similar solutions to the curve shortening flow in the plane.
Helicoidal surfaces rotating/translating under the mean curvature flow
We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new
Self-similar solutions to the mean curvature flow in the Minkowski plane $\mathbf R^{1,1}$
We introduce the mean curvature flow of curves in the Minkowski plane $\mathbf R^{1,1}$ and give a classification of all the self-similar solutions. In addition, we describe five other exact
The SLE trace is a continuous path
This is a nal project in the class 18.177 - Stochastic Processes in Physics. A proof of the fact that the SLE trace is a continuous path will be given in the case 6 8, following the argument in [RS].