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.

Cross curvature flow on locally homogenous three-manifolds (I) (with Yilong Ni and Laurent Saloff-Coste), Pacific J. Math. 236 no. 2 (2008), 263–281.

Differential Harnack estimates for backward heat equations with potentials under the Ricci flow, J. Funct. Anal. 255 no. 4 (2008), 1024–1038.

Last modified: August 18, 2008