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.^[1] He obtained his PhD in 1991 at the University of California, Berkeley with Lawrence Craig Evans as supervisor.^[2] 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,^[3] and was resolved at the same time in greater generality by Hubert Bray using alternative methods.^[4]

In 2001, Huisken and Ilmanen made a conjecture on the mathematics of general relativity, about the curvature in spaces with very little mass. This^{[clarification needed]} was proved in 2023 by Conghan Dong and Antoine Song.^[5]

He received a Sloan Fellowship in 1996.^[6]

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

• 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.