Peter W. LiChancellor's Professor, Mathematics |
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Research Interests |
Differential geometry and partial differential equations | |
| URL | math.uci.edu/~pli/ | |
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Academic Distinctions |
Fellow of the American Academy of Arts and Sciences. ISI highly cited researcher (2002). Invited speaker at the International Congress of Mathematicians, Beijing (2002). John Simon Guggenheim Fellowship (1989-1990). Alfred P. Sloan Fellowship (1982-1983). |
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| Appointments |
1991-present: Professor, Department of Mathematics, UC Irvine. 1989-1991: Professor, University of Arizona. 1985-1989: Professor, University of Utah. 1982-1985: Associate Profesor, Purdue University. 1980-1983: Assistant Professor, Stanford University. 1979-1980: Research Member, Institute for Advanced Study. |
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Research Abstract |
Primary research interest is in geometric analysis. In particular, the application of partial differential equations to the study of geometry. Topics of current research include eigenvalue problems on compact Riemannian manifolds, harmonic functions and the heat equation on complete manifolds, harmonic mappings between complete manifolds, analysis on singular algebraic varieties, and the prescribed curvature equation. | |
| Publications |
(with L. F. Tam) "Harmonic functions and the structure of complete manifolds". J. Diff. Geom. 35 (1992), pp 359-383. |
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"Harmonic sections of polynomial growth". Math. Research Letters 4 (1997), pp 35-44. |
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(with J. Wang) "Convex hull properties of harmonic maps". J. Diff. Geom. 48 (1998), pp 497-530. |
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(with J. Wang) "Counting dimensions of L-harmonic functions". Annals Math. 152 (2000), pp 645-658. |
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(with J. Wang) "Counting massive sets and dimensions of harmonic functions". J. Diff. Geom. 53 (1999), pp 237-278. |
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(with J. Wang) "Holder estimates and regularity for holomorphic and harmonic functions". J. Diff. Geom. 58 (2001), 309-329. |
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(with J. Wang) "Minimal hypersurfaces with finite index". Math. Research Letters 9 (2002), 95-103. |
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(with J. Wang) "Finiteness of disjoint minimal graphs". Math. Research Letters 8 (2001), 771-777. |
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(with J. Wang) "Complete manifolds with positive spectrum". J. Diff. Geom. 58 (2001), 501-534. |
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"Differential geometry via harmonic functions". Proc. ICM 2002 - Beijing Vol. II (2002), 293-302. |
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Professional Society |
American Mathematical Society |
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| Link to this profile | http://www.faculty.uci.edu/profile.cfm?faculty_id=2058 | |
| Last updated | 01/24/2009 | |