Tom Ilmanen

Tom Ilmanen (1961–2025 ) was an American mathematician specializing in differential geometry and the calculus of variations. He was 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 their 2001 paper,

In an influential 1995 preprint, Ilmanen made the following conjecture:

This has become known as the "multiplicity-one" conjecture. Richard Bamler and Bruce Kleiner proved the multiplicity-one conjecture in a 2023 preprint.

Ilmanen 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.