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

Email

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 KŠhler manifolds and positivity of spectrum. J. Diff. Geom. 69 (2005), 43-74.
  • (with J. Wang) Weighted PoincarŽ inequality and rigidity of complete manifolds.  Ann. Scient. ƒc. Norm. Sup., 4e sŽrie, t. 39 (2006), 921-982
  • (with S. Kong and D. Zhou) Spectrum of the Laplacian on quaternionic KŠhler manifolds. J. Diff. Geom. 78 (2008), 295-332.
  • (with J. Wang) Connectedness at infinity of complete KŠhler manifolds, To appear in Amer. J. Math. (pdf file)
  • (with L. Ji and J. Wang) Ends of locally symmetric spaces with maximal bottom spectrum, To appear in J. Reine Angew. Math. (Crelles). (pdf file)
  • (with J. Wang) A generalization of ChengŐs theorem. To appear in Asian J. Math. (pdf file)
  • (with J. Wang) Counting cusps on complete manifolds of finite volume. (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. ŇHandbook of Geometric Analysis, No. 1Ó Advanced Lectures in Mathematics, Vol. 7 (2008), International Press. (pdf file)

Unpublished Paper

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

Editorial Memberships

Seminars and Conferences

Links to Other Websites