Huai-Dong Cao
A. Everett Pitcher Professor of Mathematics

Department of Mathematics         Phone: (610) 758-3726
Lehigh University                         Fax: (610) 758-3767 

Bethlehem, PA 18015                 Email: huc2@lehigh.edu

                                       

• BA, Tsinghua (Beijing), 1981
• M.A., Princeton, 1983
• Ph.D., Princeton, 1986

• A Complete Proof of the Poincaré and Geometrization Conjectures - Application of the Hamilton-Perelman theory of the Ricci flow, with Xi-Ping Zhu, Asian J. Math. 10 (2006), no.2, 165-492.   (View Erratum to the paper)
  
• Matrix Li-Yau-Hamilton estimate for the heat equation on Kaehler manifolds,  with L. Ni, Math. Ann. 331 (2005), 795-807.
• On dimension reduction in the Kaehler-Ricci flow, Comm. Anal. Geom.  12 (2004), 305-320
  
• Ricci flow on compact Kaehler manifolds with positvie bisectional curvature, with B.-L. Chen and X.-P. Zhu,  C. R. Acad. Sci. Paris Ser. I Math.  337 (2003), 781-784.
• DGBV algebras and mirror symmetry, with Jian Zhou, Proceedings of the First International Congress of Chinese Mathematicians (Beijing, 1998), AMS/IP Studies in Advanced Mathematics, 20 (2001), 279-289.
• Gradient Kaehler-Ricci solitons and periodic orbits, with Richard S. Hamilton, Comm. Anal. Geom. 8 (2000), no.3, 517-529.
• Recent developments on the Ricci flow, with Ben Chow, Bull. Amer. Math. Soc. 36 (1999), 59-74.
• The structure of stable minimal hypersurfaces in Rⁿ⁺¹, with Y. Shen and S. Zhu, Math. Res. Lett. 4 (1997), 637-645.
• Limits of solutions to the Kaehler-Ricci flow, J. Differential Geometry 45 (1997), 257-272.
• Existence of gradient Kaehler-Ricci solitons, Elliptic and Parabolic Methods in Geometry, A.K. Peters, (1996) 1-16.
• On Harnack's inequalities for the Kaehler-Ricci flow, Invent. Math. 109 (1992), no. 2, 247--263.
• Deformation of Kaehler metrics to Kaehler-Einstein metrics on compact Kähler manifolds, Invent. Math. 81 (1985), no. 2, 359--372.

Recent  Preprints

• A compactness result for Kaehler-Ricci solitons, with Natasa Sesum, preprint (math.DG/0504526)
  
• Gaussian densities and stability for some Ricci solitons, with Richard S. Hamilton and Tom Ilmanen, preprint (math.DG/0404165)
• Kaehler-Ricci solitons on compact complex manifolds with  c_1(M)>0, with G. Tian and X. Zhu, to appear in GAFA.
  
• Supersymmetry in Calabi-Yau geometry, with J. Zhou,  to appear in Asian J. Math. 
  

Editorial Board

• Managing Editor, Journal of Differential Geometry    
  

Recent Conferences

• Workshop on Geometric Flows: Theory and Computation, IPAM, Los Angeles,  Feb. 23-27, 2004.
• Great Lakes Geometry Conference, University of Notre Dame, April 17-18, 2004.
• Lehigh University Geometry and Toplogy Conference, June 10-12, 2004.
• Texas Geometry and Topology Conference, College Station, TX, October 29-31, 2004.
  
• 7th Pacific Rim Geometry Conference, Shanghai, China, December 13-16, 2004.
• Third International Congress of Chinese Mathematicians, Hong Kong, December 17-22,  2004.
• Midwest Geometry Conference, Ohio State University, Columbus, Ohio, April 29-May 1, 2005
• Mini-Workshop: Aspects of Ricci-Flow, Oberwolfach, Germany, May 1-7, 2005
• 6th JDG Harvard Conference on Geometry and Topology, Cambridge, MA,  May 13-15, 2005
• Workshop on Flows in Geometry, Cambridge, MA, May 15-16, 2005
  

• MathSciNet

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