Minicourse: Motion by Mean Curvature

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Title: Motion of Level Sets by Mean Curvature, II
Series: Transactions of the American Mathematical Society
Author: L.C. Evans and J. Spruck
Vol. 330, No. 1, March 1992, pp 321-332

Comments

Our main goal will be to go through the short paper cited above very carefully. In that paper the authors present a new, elementary, and fairly concise proof of short time existence for the classical motion of a smooth hypersurface evolving according to its mean curvature. The proof proceeds by writing down a uniformly parabolic nonlinear equation that encodes the motion. The study of this equation makes use of classical work by Ladyzhenskaja, Solonnikov and Ural'tseva. Using norms introduced by these authors a fixed point argument is used to obtain the desired solution. As time permits, we will look at other papers on this subject such as the paper Motion of Level Sets by Mean Curvature I, also by Evans and Spruck.