Papers
A simpler proof of Frank and Lieb's sharp inequality on the Heisenberg group (joint with Fengbo Hang), preprint.
A Sharp Inequality Relating Yamabe Invariants on Asymptotically Poincare-Einstein Manifolds with a Ricci Curvature Lower Bound (joint with Zhixin Wang), preprint.
On a Sharp Inequality Relating Yamabe Invariants on a Poincare-Einstein Manifold (joint with Zhixin Wang), Proc. AMS. 150 (2022), no. 11, 4923-4929.
Uniqueness Results on a geometric PDE in Riemannian and CR Geometry Revisited , Math.Z. 301 (2022), no. 2, 1299-1314.
Remarks on an Inequality for Closed Hypersurfaces in Complete Manifolds with Nonnegative Ricci Curvature , to appear in Annales de la Faculte des Sciences de Toulouse.
Improved Sobolev inequality with constraints (joint with Fengbo Hang), IMRN 2022, no. 14, 10822-10857.
Liouville type theorems on manifolds with nonnegative curvature and strictly convex boundary (joint with Qianqiao Guo and Fengbo Hang), Math. Res. Lett. 28 (2021), no. 5, 1419-1439.
Uniqueness results for positive harmonic functions on Bn satisfying a nonlinear boundary condition (joint with Qianqiao Guo), Calculus of Variations and PDE 59 (2020), no. 5, Paper No. 146, 8 pp.
On compact Riemannian manifolds with convex boundary and Ricci curvature bounded from below , J. Geom. Anal. 31 (2021), no. 4, 3988-4003.
Remarks on a mean field equation on S2 , (joint work with Changfeng Gui, Fengbo Hang and Amir Moradifam). Journal of Mathematical Study, 54 (2021), no. 1, 81-88. (special issue for 70th birthdays of Professor Alice Chang and Paul Yang)
Uniqueness results on surfaces with boundary , Calculus of Variations and PDE 56 (2017), no. 3, Paper No. 87, 11 pp.
An integral formula in Kahler geometry with applications , Comm. Contemporary Math. 19 (2017), no. 5, 1650063, 12 pp.
Brendle's inequality on static manifolds (joint with Ye-Kai Wang), Journal of Geom. Anal. 28 (2018), no. 1, 152-169.
Characterization by symmetry of solutions of a nonlinear subelliptic equation on the Heisenberg group (joint with Yazhou Han and Meijun Zhu), J. Math. Study 50 (2017), no. 1, 17-27.
Boundary effect of Ricci curvature (joint work with Pengzi Miao), J. Diff. Geom. 103 (2016), 59-82.
Some recent results in CR geometry , Tsinghua lectures in mathematics, 469-484, Adv. Lect. Math. (ALM), 45, Int. Press, Somerville, MA.
On a remarkable formula of Jerison and Lee in CR geometry , Math. Res. Letters. 22 (2015), no.1, 279-299.
The isoperimetric constant of symmetric spaces of noncompact type , Proc. AMS.143 (2015), no.11, 4885-4891.
A new characterization of the CR sphere and the sharp eigenvalue estimate for the Kohn Laplacian ( joint with Song-Ying Li, Duong Ngoc Son), Advances in Math. 281 (2015), 1285-1305.
An Obata-type theorem in CR geometry ( joint with Song-Ying Li), J. Diff. Geom. 95 (2013), 483-502.
Pinching theorems for the volume entropy ( joint with Francois Ledrappier), preprint, 2011.
Bottom of the spectrum of Kahler manifolds with strongly pseudo-convex boundary ( joint with Song-Ying Li), IMRN 19 (2012), 4351-4371.
Compactifications of complete Riemannian manifolds , Surveys in Geometric Analysis and relativity ALM 20, pp. 517-529.
Local gradient estimate for p-harmonic functions on Riemannian manifolds (joint with Lei Zhang), to appear in Comm. Anal. Geom. 19 (2011), no. 4, 759-771.
An integral formula for the volume entropy with applications to rigidity (joint with Francois Ledrappier), Journal Diff. Geom. 85 (2010), 461-478.
Extension of a theorem of Shi and Tam (joint with Michael Eichmair and Pengzi Miao), Calculus of Variations and PDE. 43 (2012), no. 1-2, 45-56.
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
Notes on Perelman's paper on the entropy formula for Ricci flow and its geometric applications (joint with Natasa Sesum and Gang Tian), 2003.