My research interests are Several Complex Variables and Complex Geometry.
In particular, I have been working on the rigidity of holomorphic maps, the Bergman and Szegő projections, the ∂¯-equation, the geometric flows on Kaehler manifolds and related problems.
Publications
1. Flatness of CR submanifolds in a sphere (with S. Ji) Science China Mathematics 53 (2010), no. 3, 701-718. (special issue dedicated to Professor Yang Lo)
2. On the convergence of a modified Kähler-Ricci flow Mathematische Zeitschrift 268 (2011), no. 1-2, 281-289.
3. Rigidity for local holomorphic isometric embeddings from 𝔹^n into 𝔹^{N1}ו••×𝔹^{Nm} (with Y. Zhang) Journal of Differential Geometry 90 (2012), no. 2, 329-349.
4. Metric flips with Calabi ansatz (with J. Song) Geometric and Functional Analysis 22 (2012), no. 1, 240-265.
5. The Kähler-Ricci flow on singular Calabi-Yau varieties (with J. Song) ALM 21, Advances in Geometric Analysis, 119-138, Int. Press, Somerville, MA, 2012. (volume dedicated to Professor Shing-Tung Yau)
6. Holomorphic isometry from a Kähler manifold into a product of complex projective manifolds (with X. Huang) Geometric and Functional Analysis 24 (2014), no. 3, 854-886.
7. Submanifolds of Hermitian symmetric spaces (with X. Huang) Analysis and Geometry, 197-206, Springer Proc. Math. Stat., 127, Springer, Cham, 2015. (volume in honour of M. Salah Baouendi)
8. Holomorphic line bundles over a tower of coverings (with J. Zhu) Journal of Geometric Analysis 26 (2016), no. 3, 2013-2039.
9. CR Submanifolds with vanishing second fundamental forms (with Y. Zhang) Geometriae Dedicata 183 (2016), 169-180.
10. Kähler submanifolds and the Umehara algebra (with X. Cheng, A. J. Di Scala) International Journal of Mathematics 28 (2017), no. 4, 1750027, 13pp.
11. On local holomorphic maps preserving invariant (p, p)-forms between bounded symmetric domains Mathematical Research Letters 24 (2017), no. 6, 1875-1895.
12. Holomorphic isometries between products of complex unit balls (with S.-T. Chan, M. Xiao) International Journal of Mathematics 28 (2017), no. 9, 1740010, 27pp.
13. Complexity of holomorphic maps from the complex unit ball to classical domains (with M. Xiao) Asian Journal of Mathematics 22 (2018), no. 4, 729-760. (special issue in honor of Professor Ngaiming Mok)
14. Diameter rigidity for Kähler manifolds with positive bisectional curvature (with G. Liu) Mathematische Zeitschrift 290 (2018), no. 3-4, 1055-1061.
15. Holomorphic isometries from the Poincaré disk into bounded symmetric domains of rank at least two (with S.-T. Chan) Annales de I'Institut Fourier 69 (2019), no. 5, 2205-2240.
16. Local holomorphic isometries, old and new results Proceedings of the Seventh International Congress of Chinese Mathematicians. Vol. II, 409-419, Adv. Lect. Math. (ALM), 44, Int. Press, Somerville, MA, 2019.
17. Holomorphic maps from the complex unit ball to type IV classical domains (with M. Xiao) Journal des Mathématiques Pures et Appliquées (9) 133 (2020), 139-166.
18. The CR immersion into a sphere with the degenerate CR Gauss map (with W. Yin, Y. Zhang) Journal of Geometric Analysis 30 (2020), no. 1, 526-550.
19. L^p regularity of the Bergman Projection on domains covered by the polydisc (with L. Chen, S. G. Krantz) Journal of Functional Analysis 279 (2020), no. 2, 108522.
20. Finding the determinant of a matrix via complex analysis (with S.-T. Chan) American Mathematical Monthly 127 (2020), no. 6, 530-536.
21. On the canonical solution of ∂̄ on polydisks (with M. Jin) Comptes Rendus Mathématique 358 (2020), no. 5, 523-528.
22. A new geometric flow over Kähler manifolds (with Y. Li, Y. Zhang) Communications in Analysis and Geometry 28 (2020), no. 6, 1251-1288.
23. Local curvature estimates along the κ-LYZ flow (with Y. Li) Journal of Geometry and Physics 164 (2021), 104162.
24. Bergman metric on the symmetrized bidisc and its consequences (with G. Cho) International Journal of Mathematics 33 (2022), no. 10-11, Paper No. 2250071, 16 pp.
25. Bergman projection on the symmetrized bidisk (with L. Chen, M. Jin) Journal of Geometric Analysis 33 (2023), no. 7, Paper No. 204, 15pp.
26. Complex submanifolds of indefinite complex space forms (with X. Cheng, Y. Hao, X. Zhang) Proceedings of the American Mathematical Society 152 (2024), no. 6, 2541-2550.
27. Stein's theorem on infinite type domains (with L. Chen) Communications in Analysis and Geometry 32 (2024), no. 5, 1233-1254.
28. Local holomorphic isometric maps from the complex unit ball into a product of complex unit balls: negative conformal constants (with X. Cheng, Y. Hao, X. Zhang) Mathematische Annalen 391 (2025), no. 4, 6187–6203.
29. On local holomorphic maps between Kähler manifolds preserving (p,p)-forms (with S.-T. Chan) Annali della Scuola Normale Superiore di Pisa (5) 26 (2025), no. 2, 619-644.
Miscellaneous:
1. Problems on the geometric function theory in several complex variables and complex geometry October 2010, Ph.D. thesis, Rutgers.
2. A note on Bourgain's theorem
3. Uniform estimates of the Cauchy-Riemann equation on product domains
Employment
May 2025 - Professor, Westlake University
August 2013 - May 2025 Assistant Professor ('13-'19), Associate Professor ('19-'25), Professor ('25), Syracuse University
2016 Spring Research Member, Mathematical Sciences Research Institute
July 2010 - May 2013 J. J. Sylvester Assistant Professor, Johns Hopkins University
Education
2000 - 2004 Peking University, BA
2004 - 2005 graduate student, Indiana University, Bloomington
2005 - 2010 Rutgers University, New Brunswick, PhD