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American mathematician
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.
[1] Presently he is Professor Emeritus at
University of California, Irvine ,
[2] 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
[3] and a
Sloan Research Fellowship .
[4] In 2002, he was an invited speaker in the Differential Geometry section of the
International Congress of Mathematicians in Beijing,
[5] 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 ,
[6] 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 .
[7]
Li, Peter;
Yau, Shing Tung (1980). "Estimates of eigenvalues of a compact Riemannian manifold". In
Osserman, Robert ;
Weinstein, Alan (eds.). Geometry of the Laplace Operator . University of Hawaii, Honolulu (March 27–30, 1979). Proceedings of Symposia in Pure Mathematics. Vol. 36. Providence, RI:
American Mathematical Society . pp. 205–239.
doi :
10.1090/pspum/036 .
ISBN
9780821814390 .
MR
0573435 .
Zbl
0441.58014 .
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 .
JSTOR
2374257 .
MR
0630777 .
Zbl
0484.53035 .
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.
Bibcode :
1982InMat..69..269L .
doi :
10.1007/BF01399507 .
MR
0674407 .
S2CID
123019753 .
Zbl
0503.53042 .
Li, Peter;
Yau, Shing Tung (1983).
"On the Schrödinger equation and the eigenvalue problem" .
Communications in Mathematical Physics . 88 (3): 309–318.
Bibcode :
1983CMaPh..88..309L .
doi :
10.1007/BF01213210 .
MR
0701919 .
S2CID
120055958 .
Zbl
0554.35029 .
Li, Peter;
Schoen, Richard (1984).
"Lp and mean value properties of subharmonic functions on Riemannian manifolds" .
Acta Mathematica . 153 (3–4): 279–301.
doi :
10.1007/BF02392380 .
MR
0766266 .
Zbl
0556.31005 .
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 .
MR
0834612 .
Zbl
0611.58045 .
Li, Peter; Tam, Luen-Fai (1991). "The heat equation and harmonic maps of complete manifolds".
Inventiones Mathematicae . 105 (1): 1–46.
Bibcode :
1991InMat.105....1L .
doi :
10.1007/BF01232256 .
MR
1109619 .
S2CID
120167884 .
Zbl
0748.58006 .
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 .
MR
1158340 .
Zbl
0768.53018 .
Li, Peter (2012). Geometric analysis . Cambridge Studies in Advanced Mathematics. Vol. 134. Cambridge:
Cambridge University Press .
doi :
10.1017/CBO9781139105798 .
ISBN
978-1-107-02064-1 .
MR
2962229 .
Zbl
1246.53002 .
International National Academics Other