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I am working on geometric analysis, the interface of various nonlinear partial differential equations and differential geometry.
My current Research Interests involve
Geometric variational problems,
Geometric flows,
Singular/Degenerate equations.
An almost list of my publications is available at arXiv and MathSciNet.
Email: KaiZheng@amss.ac.cn kai.j.zheng at gmail.com
University of Chinese Academy of Sciences, Beijing 100190, P.R. China
Publications and Preprints
K. Zheng The space of closed G2-structures. II. concavity and hypersymplectic structures.
Y. Wu; K. Zheng Estimates for complex singular Monge-Ampère equations via integral method.
Math. Ann. (2025). https://doi.org/10.1007/s00208-025-03225-3 [arXiv:2411.03735]
Y. L. Xu; K. Zheng The uniqueness of Poincaré type constant scalar curvature Kähler metric.
H. Z. Li; L. W. Zhang; K. Zheng Calabi flow with bounded Lp scalar curvature.
J. He; K. Zheng Hermitian Calabi functional in complexified orbits.
Internat. J. Math. 34 (2023), no. 8, Paper No. 2350047, 44 pp. [arXiv:2303.00631]
P. F. Xu; K. Zheng The space of closed G2-structures. I. Connections.
Q. J. Math. 75 (2024), no. 1, 333–390. [arXiv:2212.01812]
K. Zheng Singular scalar curvature equations. I.
[arXiv:2205.14726] 69 pages.
T. Aoi; Y. Hashimoto; K. Zheng On uniform log K-stability for constant scalar curvature Kähler cone metrics.
Comm. Anal. Geom. 33 (2025), no. 3, 701-767. [arXiv:2110.02518]
L. Li; J. Wang; K. Zheng Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors.
Bull. Soc. Math. France 148 (2020), no. 1, 51–97. [arXiv:1805.04944]
K. Zheng Existence of constant scalar curvature Kähler cone metrics, properness and geodesic stability.
[arXiv:1803.09506] 87 pages.
K. Zheng Geodesics in the space of Kähler cone metrics, II. Uniqueness of constant scalar curvature Kähler cone metrics.
Comm. Pure Appl. Math. 72 (2019), no. 12, 2621–2701. [arXiv:1709.09616]
J. Keller; K. Zheng Construction of constant scalar curvature Kähler cone metrics.
Proc. Lond. Math. Soc. (3). 117 (2018), no. 3, 527–573. [arXiv:1703.06312]
H. Yin; K. Zheng Expansion formula for complex Monge–Ampère equation along cone singularities.
Calc. Var. Partial Differential Equations 58 (2019), no. 2, Art. 50, 32 pp. [arXiv:1609.03111]
L. Li; K. Zheng Uniqueness of constant scalar curvature Kähler metrics with cone singularities, I: Reductivity.
Math. Ann. 373 (2019), no. 1-2, 679-718. [arXiv:1603.01743]
L. Li; K. Zheng Generalized Matsushima's theorem and Kähler-Einstein cone metrics.
Calc. Var. Partial Differential Equations 57 (2018), no. 2, Art. 31, 43 pp. [arXiv:1511.02410]
H. Z. Li; B. Wang; K. Zheng Regularity scales and convergence of the Calabi flow.
J. Geom. Anal. 28 (2018), no. 3, 2050–2101. [arXiv:1501.01851]
K. Zheng Kähler metrics with cone singularities and uniqueness problem.
Proceedings of ISAAC 09, Current trends in analysis and its applications, 395-408, Trends Math. Birkhäuser/Springer, Cham, 2015.
K. Zheng I-properness of Mabuchi's K-energy.
Calc. Var. Partial Differential Equations 54 (2015), no. 3, 2807-2830. [arXiv:1410.1821]
S. Calamai; D. Petrecca; K. Zheng On the geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics.
New York J. Math. 22 (2016), 1111–1133. [arXiv:1405.1211]
H. Z. Li; K. Zheng Kähler non-collapsing, eigenvalues and the Calabi flow.
J. Funct. Anal. 267 (2014), no. 5, 1593-1636. [arXiv:1309.4304]
S. Calamai; K. Zheng The Dirichlet and the weighted metrics for the space of Kähler metrics.
Math. Ann. 363 (2015), no. 3, 817-856. [arXiv:1202.6610]
S. Calamai; K. Zheng Geodesics in the space of Kähler cone metrics, I.
Amer. J. Math. 137 (2015), no. 5. 1149-1208. [arXiv:1205.0056]
X. X. Chen; K. Zheng The pseudo-Calabi flow.
J. Reine Angew. Math. 674 (2013), 195-251. [arXiv:1004.2663]
H. N. Huang; K. Zheng Stability of the Calabi flow near an extremal metric.
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 11 (2012), no. 1, 167-175. [arXiv:1007.4571]
K. Zheng Stability of Kähler-Ricci flow in the space of Kähler metrics.
Pacific J. Math. 251 (2011), no. 2, 469-497. [arXiv:1004.2695]
Regular Associate of the ICTP 2020-2025
CRM-Geometric Analysis Spring, 2024
K.C. Wong Fellow December, 2023
Marie Skłodowska-Curie Individual Fellowship No. 703949 26 May 2016 - 25 May 2018
Some postdoc/junior positions at CAS are available. APPLY HERE.
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