## Research publications

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

Expository preprints

1. On a formula of Daskalopoulos, Hamilton and Sesum. arXiv:1209.1784

2. On a paper of Daskalopoulos and Sesum. arXiv:1206.1667

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

Research preprints

4. (with Xiaodong Cao) Three-dimensional noncompact $\kappa$-solutions that are Type I forward and backward. arXiv:1606.02698.

Published

(with David Glickenstein and Feng Luo) Book review of "Ricci flow for shape analysis and surface registration: theories, algorithms and applications", by Wei Zeng and Xianfeng David Gu, Springer, 2013, xi+139 pp., in Bulletin of the American Mathematical Society, 54 (2017), 141--150.

(with Peng Lu) On kappa-noncollapsed complete noncompact shrinking gradient Ricci solitons which split at infinity. Mathematische Annalen, 366 (2016), 1195--1206.

(A48) (with Peng Lu) A bound for the order of the fundamental group of a complete noncompact Ricci shrinker. Proceedings of the American Mathematical Society, 144 (2016), 2623-2625.

(A47) (with Peng Lu) Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay. Comptes Rendus Mathematique Ser. I, 353 (2015), 1007-1009.

(A46) (with Peng Lu) Harmonic maps near the identity of $S^{n}$, Differential Geometry and its Applications, 42 (2015), 31-36.

(A45) (with Peng Lu) The linear trace Harnack quadratic on a steady gradient Ricci soliton satisfies the heat equation. Proceedings of the American Mathematical Society, 141 (2013), 2855-2857.

(A44) (with Peng Lu and Bo Yang) Integral Ricci curvature bounds along geodesics for nonexpanding gradient Ricci shrinkers. Annals of Global Analysis and Geometry, 42 (2012), 279-285.

(A43) (with Peng Lu) Some elementary consequences of Perelman's canonical neighborhood theorem. Journal of Geometric Analysis, 23 (2013), 933-937.

(A42) (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.

(A41) (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.

(A35) (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.

(A34) (with Greg Anderson) A pointwise bound for solutions of the linearized Ricci flow equation on 3-manifolds, Calculus of Variations, 23 (2005) 1-12.

(A30) (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.

(A31) (with Richard Hamilton) The Cross Curvature Flow of 3-manifolds with Negative Sectional Curvature, Turkish Journal of Mathematics, 28 (2004) 1-10.

(A29) (with Peng Lu) The maximum principle for systems of parabolic equations subject to an avoidance set, Pacific J. Math., 214 (2004) 201-222.

(A27) (with David Glickenstein and Peng Lu) Metric transformations under collapsing of Riemannian manifolds, Mathematical Research Letters, 10 (2003) 737-746.

(A26) (with Feng Luo) Combinatorial Ricci Flows on Surfaces, Journal of Differential Geometry, 63 (2003) 97-129.

(A28) 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.

(A25) (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).

(A24) (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).

(A21) (with Sun-Chin Chu) Spacetime formulation of Harnack inequalities for curvature flows of hypersurfaces, Journal of Geometric Analysis, 11, 219-231 (2001).

(A23) A gradient estimate for the Ricci-Kaehler flow, Annals of Global Analysis and Geometry 19, 321-325 (2001).

(A22) (with Robert Gulliver) Aleksandrov reflection and geometric evolution of embedded hypersurfaces, Communications in Analysis and Geometry 9, 261-280 (2001).

(A20) (with Dong-Ho Tsai) Nonhomogeneous Gauss curvature flows, Indiana University Mathematics Journal 47, 965-994 (1998).

(A19) Interpolating between Li-Yau's and Hamilton's Harnack inequalities on a surface, Journal of Partial Differential Equations (China) 11, 137-140 (1998).

(A18) (with Dong-Ho Tsai) Expansion of Convex Hypersurfaces by Non-homogeneous functions of curvature, Asian Journal of Mathematics 1, 769-784 (1997).

(A16) Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations, Communications in Analysis and Geometry 5, 389-409 (1997).

(A17) (with Richard Hamilton) Constrained and linear Harnack inequalities for parabolic equations, Inventiones Mathematicae 129, 213-238 (1997).

(A13) (with Sun-Chin Chu) A geometric approach to the linear trace Harnack inequality for the Ricci flow, Mathematical Research Letters 3, 549-568 (1996).

(A12) (with Lii-Perng Liou and Dong-Ho Tsai) Expansion of embedded curves with turning angle greater than $-\pi$, Inventiones Mathematicae 123, 415-429 (1996).

(A14) (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).

(A15) (with Dong-Ho Tsai) Geometric expansion of convex plane curves, Journal of Differential Geometry 44, 312-339 (1996).

(A11) (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).

(A10) (with Sun-Chin Chu) A geometric interpretation of Hamilton's Harnack inequality for the Ricci flow, Mathematical Research Letters 2, 701-718 (1995).

(A9) The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature, Communications on Pure and Applied Mathematics 45, 1003-1014 (1992).

(A7) (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).

(A6) On the entropy estimate for the Ricci flow on compact 2-orbifolds, Journal of Differential Geometry 33, 597-600 (1991).

(A5) The Ricci flow on the 2-sphere, Journal of Differential Geometry 33, 325-334 (1991).

(A8) On Harnack's inequality and entropy for the Gaussian curvature flow, Communications on Pure and Applied Mathematics 44, 469-483 (1991).

(A4) (with Deane Yang) Rigidity of nonnegatively curved compact quaterionic-Kaehler manifolds, Journal of Differential Geometry 29, 361-372 (1989).

(A3) Deforming convex hypersurfaces by the the square root of the scalar curvature, Inventiones Mathematicae 87, 63-82 (1987).

(A2) (with Huai-Dong Cao) Compact Kaehler manifolds with nonnegative curvature operator, Inventiones Mathematicae 83, 553-556 (1986).

(A1) Deforming convex hypersurfaces by the nth root of the Gaussian curvature Journal of Differential Geometry, 22, 117-138 (1985).