Peter Li

Peter Li

Chancellor's Professor

Department of Mathematics

University of California, Irvine

410B Rowland Hall

Irvine, CA 92697-3875

Tel: (949) 824-7049

Fax: (949) 824-7993

Research Interest

Differential Geometry and Partial Differential Equations

Curriculum Vitae

Publication List

Recent Papers

(with J. Wang) Finiteness of disjoint minimal graphs. Math. Research Letters 8 (2001), 771-777. (pdf file)
(with J. Wang) Stable minimal hypersurfaces in a nonnegatively curved manifold. J. Reine Ang. Math. (Crelles J.) 566 (2004), 215-230.
(with J. Wang) Complete manifolds with positive spectrum, II. J. Diff. Geom. 62 (2002), 143-162.
(with J. Wang) Camparison theorem for Kähler manifolds and positivity of spectrum. J. Diff. Geom. 69 (2005), 43-74.
(with J. Wang) Weighted Poincaré inequality and rigidity of complete manifolds. Ann. Scient. Éc. Norm. Sup., 4e série, t. 39 (2006), 921-982.
(with S. Kong and D. Zhou) Spectrum of the Laplacian on quaternionic Kähler manifolds. J. Diff. Geom. 78 (2008), 295-332.
(with J. Wang) Connectedness at infinity of complete Kähler manifolds, Amer. J. Math. 131 (2009), 771-817.
(with L. Ji and J. Wang) Ends of locally symmetric spaces with maximal bottom spectrum. J. Reine Angew. Math. (Crelles) 632 (2009), 1-35. (pdf file)
(with J. Wang) A generalization of Cheng’s theorem. Asian J. Math. 12 (2008), 519-526.
(with J. Wang) Counting cusps on complete manifolds of finite volume. Math. Research Letters. 17 (2010), 675-688. (pdf file)

Lecture Notes and Survey Articles

"Lecture Notes on Geometric Analysis." Lecture Notes Series No. 6, Research Institute of Mathematics, Global Analysis Research Center, Seoul National University, Korea (1993). (pdf file)
Curvature and function theory on Riemannian manifolds. Surveys in Differential Geometry: Papers dedicated to Atiyah, Bott, Hirzebruch, and Singer Vol VII, International Press (2000), 375-432. (pdf file)
Differential geometry via harmonic functions. Proc. ICM 2002 - Beijing Vol. II (2002), 293-302. (pdf file)
Harmonic functions and applications to complete manifolds, Lecture notes. (pdf file)
Harmonic functions on complete Riemannian Manifolds. “Handbook of Geometric Analysis, No. 1” Advanced Lectures in Mathematics, Vol. 7 (2008), International Press. (pdf file)

· Structure of Complete Manifolds with Positive Spectrum. Preprint. (pdf file)

· Lectures on Harmonic Maps. Manuscript. (pdf file)

Unpublished Paper

(with L. Karp) The heat equation on complete Riemannian manifolds. (pdf file)

Editorial Memberships

Editor of Communications in Analysis and Geometry
Editor of Asian Journal of Mathematics
Editor of CUBO

Seminars and Conferences

Links to Other Websites