Publications/Accepted papers of Chi Li

1. Constant scalar curvature Kähler metric obtains the minimum of K-energy , International Mathematics Research Notices 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 Kähler-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 Kähler-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 Kähler-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 "Kähler-Einstein metrics with edge singularities by T. Jeffres, R.Mazzeo and Y.A.Rubinstein" (with Yanir 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. Kähler-Einstein metrics and volume minimization (with Yuchen Liu), Adv. Math. 341 (2019),440-492.


14. Quasi-projectivity of the moduli space of smooth Kähler-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), J. Eur. Math. Soc. (JEMS) 22 (2020), no.8, 2573-2627.


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 Kähler-Einstein Fano varieties (with Xiaowei Wang and Chenyang Xu), Duke Math. J. 168 (2019), no. 8, 1387-1459.


18. Orbifold regularity of weak Kähler-Einstein metrics (with Gang Tian), Advances in complex geometry , 169-178, Contemp. Math., 735, Amer. Math. Soc. 2019. arXiv:1505.01925.


19. On the stability of extensions of tangent sheaves on Kähler-Einstein Fano/Calabi-Yau pairs , Math. Ann. 381 (2021), no.3-4, 1943-1977. arXiv:1803.01734.


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


21. 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


22. On the Yau-Tian-Donaldson conjecture for singular Fano varieties (with Gang Tian and Feng Wang), Comm. Pure Appl. Math. , 74 (2021), no.8, 1748-1800. arXiv.1711.09530.


23. Algebraicity of metric tangent cones and equivariant K-stability (with Xiaowei Wang and Chenyang Xu), J. Amer. Math. Soc. 34 (2021), no.4, 1175-1214. arXiv:1805.03393.


24. Geodesic rays and stability in the cscK problem , accepted by Annales Scientifiques de l'ENS (4) 55 (2022), no.6, 1529-1574. arXiv:2001.01366.


25. The uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties (with Gang Tian and Feng Wang), Peking Math. J. 5 (2022), no.2, 383-426. arXiv:1903.01215.


26. On the Yau-Tian-Donaldson conjecture for generalized Kähler-Ricci soliton equations (with Jiyuan Han), accepted by Comm. Pure Appl. Math. , arXiv:2006.00903.


27. G-uniform stability and Kähler-Einstein metrics on singular Fano varieties, Invent. Math. , 227 (2022), no. 2, 661-744.


28. Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties (with Jiyuan Han), accepted by Geometry and Topology , arXiv:2009.01010.


29. K-stability and Fujita approximation, arXiv:2102.09457, to be published in Volume: Birational Geometry, Kähler-Einstein Metrics and Degenerations, Springer Proceedings in Mathematics & Statistics.


30. Analytical approximations and Monge-Ampère masses of plurisubharmonic singularities , to appear in International Mathematics Research Notices , arXiv:2012.15599.


31. Polarized Hodge structures for Clemens manifolds , accepted by Mathematische Annalen , arXiv:2202.10353.

Preprints

• Kähler structures for holomorphic submersions , arXiv:2302.07220.

Notes

• Non-Archimedean methods for canonical Kähler metrics , Summer School, Le Croisic 2023.


• Canonical Kähler metrics and stability of algebraic varieties , contribution to Proceedings of ICM 2022, Slides.


• Algebraic uniqueness of Kähler-Ricci flow limits on Fano varieties , Smith Colloquium, The University of Kansas, December 2021.


• Notes on weighted Kähler-Ricci solitons and application to Ricci-flat Kähler cone metrics , slides of talk , Xiamen International Conference on Geometric Analysis, June 2021.
  AMS sectional meeting talk slides (Oct 2021)


• Recent progress on the YTD conjecture for cscK metrics , CUNY Geometric Analysis Seminar, April, 2021.


• K-stability and restricted volumes , Purdue Algebraic Geometry seminar, November, 2020.


• An inhomogeneous optimal degeneration problem for Fano varieties , Simons Conference on K-stability, September, 2020.


• Generalized YTD conjecture on Fano varieties , Workshop on Geometric Analysis, September, 2020.


• Geodesic rays and stability in the cscK problem , BICMR on-line seminar talk slides, April, 2020.


• Topics on Kähler-Einstein metrics , talk slides, December, 2019.


• Algebraicity of metric tangent cones , talk slides.


• On Yau-Tian-Donaldson conjecture for singular Fano varieties , slides for the talk in J. Cheeger's 75th Birthday Conference, 2018.


• Moduli space of smoothable Kahler-Einstein Q-Fano varieties talk slides at Trends in Modern Geometry , University of Tokyo, 2015


• Job talk slides


• Defense slides .


• On rotationally symmetric Kähler-Ricci solitons. arXiv:1004.4049.


• Notes on Sean Paul paper 2010


• Notes on Futaki invariant 2007


• Notes on Family Index Theorem (after Bismut) 2004


• Master Thesis (Chinese) 2007