Cao Huaidong

Cao Huaidong , also known as Huai-Dong Cao ( Chinese 曹懷東 / 曹怀东 , Pinyin Cáo Huáidōng ; born November 8, 1959 in Jiangsu ) is a Chinese mathematician who deals with differential geometry .

Cao studied at Tsinghua University ( bachelor's degree in 1981) and at Princeton University ( master's degree in 1983), where he received his doctorate in 1986 with Shing-Tung Yau . From 1987 he was an assistant professor at Columbia University . In 1993 he became Associate Professor and in 1999 Professor at Texas A&M University , which he remained until 2004. In 2002/3 he was co-director at UCLA's IPAM . He has been an Everett Pritcher Professor at Lehigh University since 2003 . Among other things, he was visiting scholar and visiting professor at the Massachusetts Institute of Technology (1999), Harvard University (2000), IHES (2001), ETH Zurich , Isaac Newton Institute (2001), and the Max Planck Institute for Mathematics in Bonn (2001), at the MSRI (1986/87) and the University of Pisa . In 1992/93 he was at the Institute for Advanced Study .

Cao dealt, among other things, with Ricci rivers and was with Zhu Xiping part of one of the three teams that examined, worked out and completed Grigori Perelman's proof of the Poincaré conjecture .

From 1991 to 1993 he was a Sloan Research Fellow and in 2004 a Guggenheim Fellow. He is the executive editor of the Journal of Differential Geometry.

Fonts (selection)

Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds. Invent. Math. 81 (1985) no. 2, 359-372
with Chow: Compact Kähler manifolds with non-negative curvature operator. Invent. Math. 83 (1986) no. 3, 553-556.
mit Mok: Holomorphic immersions between compact hyperbolic space forms. Invent. Math. 100 (1990) no. 1, 49-61.
On Harnack's inequalities for the Kähler-Ricci flow. Invent. Math. 109 (1992) no. 2: 247-263.
Limits of solutions to the Kähler-Ricci flow. J. Differential Geom. 45 (1997), no. 2, 257-272.
with Shen, S.Zhu: The structure of stable minimal hypersurfaces in . ${\ displaystyle \ mathbb {R} ^ {n + 1}}$ Math. Res. Lett. 4 (1997), no. 5, 637-644.
with X.Zhu: A complete proof of the Poincaré and geometrization conjectures — application of the Hamilton-Perelman theory of the Ricci flow. Asian J. Math. 10 (2006), no. 2, 165-492.
with Zhou: On complete gradient shrinking Ricci solitons. J. Differential Geom. 85 (2010), no. 2, 175-185

↑ Published in Cao, Zhu: A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton – Perelman theory of the Ricci flow. In: Asian Journal of Mathematics. Volume 10, 2006, pp. 165-492, Erratum pp. 663-664 Online, pdf