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]
Tom Ilmanen | |
|---|---|
| Born | 1961 |
| Nationality | American |
| Education | Ph.D. in Mathematics |
| Alma mater | University of California, Berkeley |
| Occupation | Mathematician |
| Known for | Research in differential geometry, proof of Riemannian Penrose conjecture |
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.
Selected publications
edit- 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.
References
edit- ^ Switzerland, ETH Zürich Professur für Mathematik HG G. 62 3 Rämistrasse 101 8092 Zürich. "Tom Ilmanen". math.ethz.ch.
{{cite web}}: CS1 maint: numeric names: authors list (link) - ^ Tom Ilmanen at the Mathematics Genealogy Project
- ^ Differential Geometry: Partial Differential Equations on Manifolds. (1993). In R. Greene & S.-T. Yau (Eds.), Proceedings of Symposia in Pure Mathematics. American Mathematical Society. https://doi.org/10.1090/pspum/054.1 https://doi.org/10.1090/pspum/054.1
- ^ Mars, M. (2009). "Present status of the Penrose inequality". Classical and Quantum Gravity (Vol. 26, Issue 19, p. 193). IOP Publishing.
- ^ Nadis, Steve (30 November 2023), "A Century Later, New Math Smooths Out General Relativity", Quanta Magazine
- ^ "Fellows Database | Alfred P. Sloan Foundation". sloan.org.