Research Interests
- differential geometry, geometric analysis and PDE
Papers
- An integral formula for the volume entropy with an application to rigidity (joint with François Ledrappier), submitted.
- Boundary effect on Compact Manifolds with Nonnegative Scalar Curvature-- a generalization of a theorem of Shi and Tam (joint with Michael Eichmair and Pengzi Miao), submitted.
- Rigidity Theorems for Compact Manifolds with Boundary and Positive Ricci Curvature (joint with Fengbo Hang), J. Geom. Anal 19 (2009), 628-642.
- A rigidity theorem for the hemishpere (joint with Fengbo Hang), preprint. (now subsumed in the paper above)
- Harmonic functions, entropy, and a characterization of the hyperbolic space, Journal Geom. Anal. 18 (2008), 272-284.
- An integral equation in conformal geometry (joint with Fengbo Hang and Xiaodong Yan), Annales de l'Institut Henri Poincare (C) 26 (2009), 1-21.
- A note on a conjecture of Schroeder and Strake (joint with Fengbo Hang), Pacific Math. Journal 232 (2007), 283-287.
- Remark on Zhong-Yang's eigenvalue estimate (joint with Fengbo Hang), Int. Math. Res. Notices 2007.
- Sharp integral inequalities for harmonic functions (joint with Fengbo Hang and Xiaodong Yan), Comm. Pure Appl. Math. 61 (2008), 54-95.
- On the stability of Kahler-Einstein manifolds (joint with Xianzhe Dai and Guofang Wei), Comm. Anal. Geom 15 (2007), 669-693.
- On asymptotically complex hyperbolic Kahler manifolds , Proc. AMS 135 (2007), no.9, 2949-2960.
- Some rigidity and nonrigidity results on the sphere (joint with Fengbo Hang), Comm. Anal. Geom. 14 (2006) no.1, 91-106.
- A new approach to some nonlinear geometric equations in dimension two (joint with Fengbo Hang), Cal. of Var. PDE. 26 (2006) no. 1, 119-135.
- On the stability of Riemannian manifolds with a parallel spinor (joint with Xianzhe Dai and Guofang Wei), Invent. Math. 161 (2005), 151-176.
- Uniqueness of the AdS spacetime in any dimensions , Acta Math. Sinica 21 (2005) no. 4, 917-922.
- On the L2 cohomology of a convex cocompact hyperbolic manifold, Duke Math. J. 115 (2002) no.2, 311-327.
- On the geometry of conformally compact Einstein manifolds, Math. Research Letters 8 (2001) no. 5&6 (2001) 671--688.
- A new proof of Lee's theorem on the spectrum of conformally compact Einstein manifolds, Comm. Anal. Geom. 10 (2002), no.3, 647-651.
- The mass of asymptotically hyperbolic manifolds, Journal Diff. Geom. 57 (2001), no.2, 273--299.
Notes