Tuesday and Thursday, 11:40am-12:55pm, February 12 to March 21
Room 205, Physics Building
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
PDF Version of the paper
William K. Allard
029A Physics Building
Phone: 660-2861 E-mail: wka@math.duke.edu
Office Hours: TBA
Introduction February 12, 2008 The magic identities February 19, 2008 Uniqueness for linear equations February 20, 2008 An efficient inverse function theorem February 20, 2008
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.
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Last modified October 19, 2007.