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The College of Arts Sciences

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Xiaodong Cao

Professor and Director of Undergraduate Studies

Xiaodong Cao

Malott Hall, Room 521

Educational Background

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



  • Mathematics

Graduate Fields

  • Mathematics


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.


  • 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.