Research publications


    Papers on ArXiv

    Reviews of papers on Math Reviews (for subscribers of MathSciNet)

  1. (with Peng Lu) The linear trace Harnack quadratic on a steady gradient Ricci soliton satisfies the heat equation. arXiv:1105.3494

  2. An elementary remark on a lower bound for the \mu-invariant of singularity models for Ricci flow. arXiv:1104.3276

  3. (with Peng Lu and Bo Yang) Integral Ricci curvature bounds along geodesics for nonexpanding gradient Ricci shrinkers. Annals of Global Analysis and Geometry, published online 07 February 2012. (arXiv:1104.1406 and arXiv:1103.5505 combined)

  4. (with Peng Lu) Some elementary consequences of Perelman's canonical neighborhood theorem. arXiv:1103.4165 Journal of Geometric Analysis, published online 15 October 2011.

  5. (with Peng Lu and Bo Yang) Lower lower bounds for the scalar curvatures of noncompact gradient Ricci solitons. Comptes Rendus Mathematique Ser. I, 349 (2011), 1265--1267. (arXiv:1102.4424 and arXiv:1102.0548 combined)

  6. (with Peng Lu and Bo Yang) A necessary and sufficient condition for Ricci shrinkers to have positive AVR. Proceedings of the American Mathematical Society, 140 (2012), 2179--2181.

  7. (with David Glickenstein and Peng Lu) Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature, Math. Zeit., 254 (2006) 1-28.

  8. (with Greg Anderson) A pointwise bound for solutions of the linearized Ricci flow equation on 3-manifolds, Calculus of Variations, 23 (2005) 1-12.

  9. (with Peng Lu) On the asymptotic scalar curvature ratio of complete Type I-like ancient solutions to the Ricci flow on non-compact 3-manifolds, Communications in Analysis and Geometry, 12 (2004) 59-91.

  10. (with Richard Hamilton) The Cross Curvature Flow of 3-manifolds with Negative Sectional Curvature, Turkish Journal of Mathematics, 28 (2004) 1-10.

  11. (with Peng Lu) The maximum principle for systems of parabolic equations subject to an avoidance set, Pacific J. Math., 214 (2004) 201-222.

  12. (with David Glickenstein and Peng Lu) Metric transformations under collapsing of Riemannian manifolds, Mathematical Research Letters, 10 (2003) 737-746.

  13. (with Feng Luo) Combinatorial Ricci Flows on Surfaces, Journal of Differential Geometry, 63 (2003) 97-129.

  14. On an alternate proof of Hamilton's matrix Harnack inequality of Li-Yau type for the Ricci flow, Indiana University Mathematics Journal, 52 (2003), 863-874.

  15. (with Dan Knopf and Peng Lu) Hamilton's injectivity radius estimate for sequences with almost nonnegative curvature operators, Communications in Analysis and Geometry 10, 1151-1180 (2002).

  16. (with Dan Knopf) New Li-Yau-Hamilton Inequalities for the Ricci Flow via the Space-time Approach, Journal of Differential Geometry 60, 1-54 (2002).

  17. (with Sun-Chin Chu) Spacetime formulation of Harnack inequalities for curvature flows of hypersurfaces, Journal of Geometric Analysis, 11, 219-231 (2001).

  18. A gradient estimate for the Ricci-Kaehler flow, Annals of Global Analysis and Geometry 19, 321-325 (2001).

  19. (with Robert Gulliver) Aleksandrov reflection and geometric evolution of hypersurfaces, Communications in Analysis and Geometry 9, 261-280 (2001).

  20. (with Dong-Ho Tsai) Nonhomogeneous Gauss curvature flows, Indiana University Mathematics Journal 47, 965-994 (1998).

  21. Interpolating between Li-Yau's and Hamilton's Harnack inequalities on a surface, Journal of Partial Differential Equations (China) 11, 137-140 (1998).

  22. (with Dong-Ho Tsai) Expansion of Convex Hypersurfaces by Non-homogeneous functions of curvature, Asian Journal of Mathematics 1, 769-784 (1997).

  23. Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations, Communications in Analysis and Geometry 5, 389-409 (1997).

  24. (with Richard Hamilton) Constrained and linear Harnack inequalities for parabolic equations, Inventiones Mathematicae 129, 213-238 (1997).

  25. (with Sun-Chin Chu) A geometric approach to the linear trace Harnack inequality for the Ricci flow, Mathematical Research Letters 3, 549-568 (1996).

  26. (with Lii-Perng Liou and Dong-Ho Tsai) Expansion of embedded curves with turning angle greater than $-\pi$, Inventiones Mathematicae 123, 415-429 (1996).

  27. (with Lii-Perng Liou and Dong-Ho Tsai) On the nonlinear parabolic equation $u_t=F(\Delta u+nu)$ on $S^n$, Communications in Analysis and Geometry 4, 415-434 (1996).

  28. (with Dong-Ho Tsai) Geometric expansion of convex plane curves, Journal of Differential Geometry 44, 312-339 (1996).

  29. (with Robert Gulliver) Aleksandrov reflection and nonlinear evolution equations, I: The n-sphere and n-ball, Calculus of Variations and PDE 4, 249-264 (1996).

  30. (with Sun-Chin Chu) A geometric interpretation of Hamilton's Harnack inequality for the Ricci flow, Mathematical Research Letters 2, 701-718 (1995).

  31. The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature, Communications on Pure and Applied Mathematics 45, 1003-1014 (1992).

  32. (with Lang-Fang Wu) The Ricci flow on compact 2-orbifolds with curvature negative somewhere, Communications on Pure and Applied Mathematics 44, 275-286 (1991).

  33. On the entropy estimate for the Ricci flow on compact 2-orbifolds, Journal of Differential Geometry 33, 597-600 (1991).

  34. The Ricci flow on the 2-sphere, Journal of Differential Geometry 33, 325-334 (1991).

  35. On Harnack's inequality and entropy for the Gaussian curvature flow, Communications on Pure and Applied Mathematics 44, 469-483 (1991).

  36. (with Deane Yang) Rigidity of nonnegatively curved compact quaterionic-Kaehler manifolds, Journal of Differential Geometry 29, 361-372 (1989).

  37. Deforming convex hypersurfaces by the the square root of the scalar curvature, Inventiones Mathematicae 87, 63-82 (1987).

  38. (with Huai-Dong Cao) Compact Kaehler manifolds with nonnegative curvature operator, Inventiones Mathematicae 83, 553-556 (1986).

  39. Deforming convex hypersurfaces by the nth root of the Gaussian curvature Journal of Differential Geometry, 22, 117-138 (1985).