Publications/Accepted papers

  1. Constant scalar curvature Kahler metric obtains the minimum of K-energy , International Mathematics Research Notice Vol.2011, No.9, pp. 2161-2175.

  2. Greatest lower bound on Ricci curvature for toric Fano manifolds. Advances in Mathematics 226(2011) 4921-4932. arXiv:0909.3443.

  3. On the limit behavior of metrics in continuity method to Kahler-Einstein problem in toric Fano case. Compositio Mathematicae 148 (2012), no.6, 1985-2003. arXiv: 1012.5229.

  4. Special test configurations and K-stability of Fano varieties. (with Chenyang Xu), Ann. of Math. (2) 180 (2014), no.1, 197-232. arXiv:1111.5398.

  5. Conical Kahler-Einstein metrics revisited (with Song Sun), Comm. Math. Phys. 331 (2014), no. 3, 927-973. arXiv:1207.5011.

  6. Numerical solutions of SO(3) invariant Kahler-Einstein metrics with cone singularities along a smooth quadric curve . Journal of Geometric Analysis , Vol.25, Issue 3 (2015), 1773-1797. arxiv:1207.6592.

  7. Remarks on logarithmic K-stability , Communications in Contemporary Mathematics , Vol. 17, Issue 02 (2015) 1450020, arXiv:1104.0428.

  8. Appendix A to "Kahler-Einstein metrics with edge singularities by T. Jeffres, R.Mazzeo and Y.A.Rubinstein" (with Y.A.Rubinstein), Annals of Mathematics, 183 (2016), pp 162-166.

  9. A Pohozaev identity and critical exponents of some complex Hessian equations , Journal of Partial Differential Equations, (2016), no.3, 175-194. arXiv:1309.5623.

  10. Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds , J. Reine Angew. Math. 733 (2017), 55-85. arXiv:1302.6681

  11. K-semistability is equivariant volume minimization , Duke Math. Journal, Vol. 166, no. 16 (2017), 3147-3218. arXiv:1512.07205.

  12. Minimizing normalized volumes of valuations , Mathematische Zeitschrift, Vol. 289, 2018, no.1-2, 491-513. arXiv:1511.08164.

  13. Kahler-Einstein metrics and volume minimization (with Yuchen Liu), Adv. Math. 341 (2019),440-492.

  14. Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds (with Xiaowei Wang and Chenyang Xu), Annales Scientifiques de l'ENS (4)51 (2018), no.3, 739-772.

  15. Stability of valuations and Kollar components , (with Chenyang Xu), accepted by J. Eur. Math. Soc. , arxiv:1604.05398.

  16. Stability of Valuations: Higher rational Rank , (with Chenyang Xu), Peking Mathematical Journal , volume 1 (2018), 1-79.

  17. On the proper moduli spaces of smoothable Kahler-Einstein Fano varieties , (with Xiaowei Wang and Chenyang Xu), Duke Math. J. 168 (2019), no. 8, 1387-1459.

  18. On the stability of extensions of tangent sheaves on Kahler-Einstein Fano/Calabi-Yau pairs , accepted by Math. Ann. , arXiv:1803.01734.

  19. On sharp rates and analytic compactifications of asymptotically conical Kahler metrics . Duke Math. J. , vol. 169 (2020), no. 8, 1397-1483. arXiv:1405.2433.

  20. A guided tour to normalized volume (with Yuchen Liu and Chenyang Xu). In Geometric Analysis, volume 333 of Progr. Math., pages 167-219. Birkauser/Springer, Cham, 2020

  21. On Yau-Tian-Donaldson conjecture for singular Fano varieties (joint with Gang Tian and Feng Wang), accepted by Comm. Pure Appl. Math. , arXiv.1711.09530.

Preprints

Notes