Biography:Peter Li (mathematician)

Short description: American mathematician

Peter Wai-Kwong Li
Born	(1952-04-18) April 18, 1952
Education	University of California, Berkeley (Ph.D.)
Awards	Guggenheim Fellowship Sloan Research Fellowship
Scientific career
Fields	Mathematics
Institutions	University of California, Irvine
Doctoral advisor	Shiing-Shen Chern Henderson Chik-Hing Yeung

Peter Wai-Kwong Li (born 18 April 1952) is an American mathematician whose research interests include differential geometry and partial differential equations, in particular geometric analysis. After undergraduate work at California State University, Fresno, he received his Ph.D. at University of California, Berkeley under Shiing-Shen Chern in 1979. Presently he is Professor Emeritus at University of California, Irvine, where he has been located since 1991.

His most notable work includes the discovery of the Li–Yau differential Harnack inequalities, and the proof of the Willmore conjecture in the case of non-embedded surfaces, both done in collaboration with Shing-Tung Yau. He is an expert on the subject of function theory on complete Riemannian manifolds.

He has been the recipient of a Guggenheim Fellowship in 1989 and a Sloan Research Fellowship. In 2002, he was an invited speaker in the Differential Geometry section of the International Congress of Mathematicians in Beijing, where he spoke on the subject of harmonic functions on Riemannian manifolds. In 2007, he was elected a member of the American Academy of Arts and Sciences, which cited his "pioneering" achievements in geometric analysis, and in particular his paper with Yau on the differential Harnack inequalities, and its application by Richard S. Hamilton and Grigori Perelman in the proof of the Poincaré conjecture and Geometrization conjecture.

Notable publications

• Li, Peter; Yau, Shing Tung (1980). "Estimates of eigenvalues of a compact Riemannian manifold". in Osserman, Robert; Weinstein, Alan. University of Hawaii, Honolulu (March 27–30, 1979). 36. Providence, RI: American Mathematical Society. pp. 205–239. doi:10.1090/pspum/036. ISBN 9780821814390. 
• Cheng, Siu Yuen; Li, Peter; Yau, Shing-Tung (1981). "On the upper estimate of the heat kernel of a complete Riemannian manifold". American Journal of Mathematics 103 (5): 1021–1063. doi:10.2307/2374257. 
• Li, Peter; Yau, Shing Tung (1982). "A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces". Inventiones Mathematicae 69 (2): 269–291. doi:10.1007/BF01399507. Bibcode: 1982InMat..69..269L. http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002098652. 
• Li, Peter; Yau, Shing Tung (1983). "On the Schrödinger equation and the eigenvalue problem". Communications in Mathematical Physics 88 (3): 309–318. doi:10.1007/BF01213210. Bibcode: 1983CMaPh..88..309L. https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-88/issue-3/On-the-Schrödinger-equation-and-the-eigenvalue-problem/cmp/1103922378.full. 
• Li, Peter; Schoen, Richard (1984). "L^p and mean value properties of subharmonic functions on Riemannian manifolds". Acta Mathematica 153 (3–4): 279–301. doi:10.1007/BF02392380. 
• Li, Peter; Yau, Shing-Tung (1986). "On the parabolic kernel of the Schrödinger operator". Acta Mathematica 156 (3–4): 153–201. doi:10.1007/bf02399203. 
• Li, Peter; Tam, Luen-Fai (1991). "The heat equation and harmonic maps of complete manifolds". Inventiones Mathematicae 105 (1): 1–46. doi:10.1007/BF01232256. Bibcode: 1991InMat.105....1L. 
• Li, Peter; Tam, Luen-Fai (1992). "Harmonic functions and the structure of complete manifolds". Journal of Differential Geometry 35 (2): 359–383. doi:10.4310/jdg/1214448079. 
• Li, Peter (2012). Geometric analysis. Cambridge Studies in Advanced Mathematics. 134. Cambridge: Cambridge University Press. doi:10.1017/CBO9781139105798. ISBN 978-1-107-02064-1. 

See also

• Ricci flow

External links

• Peter Li's website at University of California, Irvine