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Xiaodong Cao

Associate Professor

Malott Hall, Room 507

Educational Background

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



Research Focus

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.


  • Mathematics

Graduate Fields

  • Mathematics


  • The Weyl tensor of gradient Ricci solitons (with Hung Tran), Geometry & Topology, to appear.
  • Curvature pinching estimate and singularities of the Ricci flow, Communications in Analysis and Geometry 19 no. 5 (2011), 975–990.
  • The conjugate heat equation and ancient solutions of the Ricci flow (with Qi S. Zhang), Advances in Mathematics 228 no. 5 (2011), 2891–2919.
  • Differential Harnack estimates for time-dependent heat equations with potentials (with Richard Hamilton), Geom. Funct. Anal. 19 no. 4 (2009), 989–1000.
  • Differential Harnack estimates for backward heat equations with potentials under the Ricci flow, J. Funct. Anal. 255 no. 4 (2008), 1024–1038.