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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. 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.
K. Zheng Singular scalar curvature equations. I.
K. Zheng Existence of constant scalar curvature Kähler cone metrics, properness and geodesic stability.
Math. Ann. 393 (2025), no. 3-4, 3639–3711. [arXiv:1803.09506]
Y. Wu; K. Zheng Estimates for complex singular Monge-Ampère equations via integral method.
Math. Ann. 392 (2025), no. 4, 5169–5207. [arXiv:2411.03735]
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]
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]
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]
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 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]
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]
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]
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. 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]
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]
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]
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; 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]
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]
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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