Columbia Crown

Columbia University
Department of Mathematics

presents the


SAMUEL EILENBERG LECTURES


Tom Ilmanen
 ETH Zürich and Columbia University


Mean Curvature Flow


starting
Thursday September 11, 2002
507 Mathematics, 2:40-4:00 p.m.



Tea will be served each day at 4:00 p.m. in Room 508.


The lectures will treat the mean curvature flow of hypersurfaces of Euclidean space, including singularity formation, self-similar solutions, topological change, and weak solutions. There will be a strong emphasis on open problems.

A self-similarly shrinking surface in R3
Tentative Outline

Sept 11 Introduction
Sept 18 Classical results
Sept 25 -- no lecture --
Oct 2 Maximum principle formulation
Oct 9 Variational formulation I
Oct 16 Shrinking solutions I
Oct 23 Shrinking solutions II
Oct 30 Expanding solutions
Nov 6 Topological change
Nov 13 Variational formulation II
Nov 20 Stratification
Nov 27 -- Thanksgiving holiday --
Dec 4 Nonsqueezing (progress report)


Literature:

  • Mean curvature flow problem list, 2003, pdf, ps, dvi.
  • Lectures on Mean Curvature Flow and Related Equations (Trieste Notes), 1995, dvi (no graphics), ps (8 MB), gzipped ps.
  • Elliptic Regularization and Partial Regularity for Motion by Mean Curvature, 1994, dvi (no graphics), ps, gzipped ps.
  • All mathematical papers of T. Ilmanen (except some old ones) here.

    T. Ilmanen, Math Department, Columbia University, September 2003.