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

• On second variation of Perelman's Ricci shrinker entropy, with M. Zhu, Math. Ann., 353 (2012), no. 3, 747-763.
• About the Calabi problem: a finite dimensional approach, with J. Keller, to appear in J. European Math. Soc.
  
• On complete gradient shrinking Ricci solitons, with D. Zhou, J. Diffeential Geom., 85 (2010), 175-186.
  
• Recent progress on Ricci solitons, Advanced Lectures in Mathematics, 11 (2010), 1-38.
• 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. 
• 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.
• 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

• On Bach-flat gradient shrinking Ricci solitons, with Q. Chen, accepted by Duke Math. J.
  
• On the structure of gradient Yamabe solitons, with X. Sun and Y. Zhang, accepted by Math. Res. Lett.
  
• A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension, with H. Li, to appear in Calc. Var. Partial Diffrential Equations
  
• Bach-flat gradient steady Ricci solitons, with G. Catino, Q. Chen, C. Mantegazza and L. Mazzieri, arXiv:1107.4591.
• The Kahler-Ricci flow on Fano manifolds, preprint (2012)
  

Editorial Board

• Managing Editor, Journal of Differential Geometry    
  

Recent Conferences

• Yamabe Memorial Symposium (50th Anniversary): Geometric Analysis, Minneapolis, October, 2012.
• Workshop on Geometric Flows and Geometric Structures, Valencia, Spain, September 2012.
• International Conference on Geometric Analysis, Seillac, France, September 2012.
• International Conference on Complex Geometry, Singularities, and Related Fields, Beijing, China, August 2012.
• International Conference on Geometric Analysis and Nonlinear PDEs, Changsha, China, May, 2012.
• Second Workshop on Diffrential Geometry, Maceio, Brazil, February 2012.

• MathSciNet

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