Xiaodong Cao

Associate Professor of Mathematics

507 Malott Hall

(607) 255-7431

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.

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

Differential Harnack estimates for time-dependent heat equations with potentials (with Richard Hamilton), Geom. Funct. Anal. 19 no. 4 (2009), 989–1000.

The conjugate heat equation and ancient solutions of the Ricci flow (with Qi S. Zhang), Advances in Mathematics 228 no. 5 (2011), 2891–2919.

Curvature pinching estimate and singularities of the Ricci flow, Communications in Analysis and Geometry 19 no. 5 (2011), 975–990.