Tom Ilmanen

Tom Ilmanen (born 1961) is an American mathematician specializing in differential geometry and the calculus of variations. He is a professor at ETH Zurich. He obtained his PhD in 1991 at the University of California, Berkeley with Lawrence Craig Evans as supervisor. Ilmanen and Gerhard Huisken used inverse mean curvature flow to prove the Riemannian Penrose conjecture, which is the fifteenth problem in Yau's list of open problems, and was resolved at the same time in greater generality by Hubert Bray using alternative methods.

In 2001, Huisken and Ilmanen made a conjecture on the mathematics of general relativity, about the curvature in spaces with very little mass. This was proved in 2023 by Conghan Dong and Antoine Song.

He received a Sloan Fellowship in 1996.

He wrote the research monograph Elliptic Regularization and Partial Regularity for Motion by Mean Curvature.

Selected publications

 * Huisken, Gerhard, and Tom Ilmanen. "The inverse mean curvature flow and the Riemannian Penrose inequality." Journal of Differential Geometry 59.3 (2001): 353–437. DOI: 10.4310/jdg/1090349447
 * Ilmanen, Tom. "Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature." Journal of Differential Geometry 38.2 (1993): 417–461.
 * Feldman, Mikhail, Tom Ilmanen, and Dan Knopf. "Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons." Journal of Differential Geometry 65.2 (2003): 169–209.