Here are the currently linked preprints:
- Two Kazdan-Warner type identities for the renormalized volume coefficients and the
Gauss-Bonnet curvatures of a Riemannian metric, joint with Bin Guo and Haizhong Li.
This is almost the same as posted on arxiv as arXiv:0911.4649[Math DG], with minor corrections. It has been
accepted for publication in the Pacific Journal of Mathematics.
- On the prescribing $\sigma_2$ curvature equation on $\mathbb S^4$,
joint with S. -Y. Alice Chang and Paul Yang. This is the same as posted on arxiv as
arXiv:0911.0375[Math DG]. The published version is at
Calculus of Variations and PDE, 40(2011), 539-565
(published online July 7, 2010), DOI: 10.1007/s00526-010-0350-2.
- ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE sigma_k-YAMABE EQUATION NEAR
ISOLATED SINGULARITIES, joint with YanYan Li and Eduardo V. Teixeira.
This version added a reference which we learned after the paper was first posted on
arxiv as arXiv:0911.0234[Math AP]. The published version is at
Invent Math, 182(2010), 635-684 (published online Aug. 18, 2010), DOI 10.1007/s00222-010-0274-7.
On the local solvability of the Nirenberg problem on $S^2$,
Discrete and Continuous Dynamical Systems, 28(2010), 607-615, doi:10.3934/
- A Kazdan-Warner type identity for the $\sigma_k$ curvature,
published in C. R. Acad. Sci. Paris, Ser. I 342(2006), pp. 475--478.
Please note a mis-statement
in lines 2--5 of Remark 4. The correction is here.
A preprint version can be found here.
Also it has been brought to my attention that Theorem 1 in the case of
$k < n$ and $(M,g)$ locally conformally flat
had been covered in Theorem 5.2 of J. Viaclovsky's
article "Some Fully Nonlinear Equations in Conformal Geometry", Differential equations and mathematical physics (Birmingham, AL, 1999) (Providence, RI), Amer. Math. Soc., Providence, RI, 2000, pp. 425--433.
Classification of singular radial solutions to the $\sigma_k$
Yamabe equation on annular domains, joint with S. -Y. A. Chang
and P. Yang. This is the pre-print version as of June 2005. The published version
JDE, 216(2005), 482-501.
- Local pointwise estimates for
solutions of the $\sigma_2$ curvature equation on $4$ manifolds. This is the pre-print version
as of June 2004. The published version is at
IMRN, 2004, no. 79, 4269-4292.
- The existence of conformal metrics
with constant scalar curvature and constant boundary mean curvature,
Communications in Analysis and Geometry, 8 (2000), No.4, 809-869 (joint with Y. -Y Li).
The Yamabe problem on manifolds with boundary: Existence and compactness results,
Duke Mathematical Journal 99(1999), No.3, 489-542 (joint with Y.-Y Li).