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Motion by Mean Curvature

Tuesday and Thursday, 11:40am-12:55pm, February 12 to March 21

Room 205, Physics Building

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Text

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

### Instructor

William K. Allard

029A Physics Building

Phone: 660-2861 E-mail: wka@math.duke.edu

Office Hours: TBA

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Notes

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

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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.

Return to: William K. Allard's home page

Last modified October 19, 2007.