Xiaodong Cao

Assistant Professor of Mathematics

Web Site www.math.cornell.edu/~cao/ Contact Information Office:  507 Malott Hall Phone:  (607) 255-7431 Fax:  (607) 255-7149 Email:  cao@math.cornell.edu Courses & Office Hours

Education

Ph.D. (2002), Massachusetts Institute of Technology

Research Area: Differential geometry and geometric analysis

My research has been concentrated on the study of geometric evolution equations and their applications to differential geometry.  I am especially interested in the Ricci flow, its singularities, long time existence and convergence.

Selected Publications

Isoperimetric estimate for the Ricci flow on S² × S¹, Communications in Analysis and Geometry 13 no. 4 (2005), 727–739.

Eigenvalues of (–\triangle + R/2) on manifolds with nonnegative curvature operator, Mathematische Annalen 337 no. 2 (2007), 435–441.

Compact gradient shrinking Ricci solitons with positive curvature operator, Journal of Geometric Analysis 17 no. 3 (2007), 451–459.

Dimension reduction under the Ricci Flow on manifolds with nonnegative curvature operator, Pacific Journal of Mathematics (to appear).

Cross curvature flow on locally homogenous three-manifolds (with Yilong Ni and Laurent Saloff-Coste), preprint 2007.

Last modified: October 31, 2006