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Dr Kai Zheng

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Kai Zheng

Marie Curie Research Fellow

Office: B2.34
Phone: +44 (0)24 7657 3512
Email: K dot Zheng at warwick dot ac dot uk
Homepage


I am working on geometric analysis, the interface of various nonlinear partial differential equations and differential geometry, specially complex geometry. The analytic tools include calculus of variations, higher order geometric flows and complex Monge-Ampère equations.

Here is my Curriculum Vitae.

My current research involves regularity/singularity phenomena of geometric PDEs, existence/uniqueness of critical metrics and convergence of geometric flows.

An almost list of my publications/preprints is available at arXiv and MathSciNet.

Co-organise:
Junior Warwick-Imperial-Cambridge geometric analysis seminar. Queen Mary University of London, January 5-8, 2016.

Teaching Responsibilities:

2016/17 TERM 1: MA4A2 Advanced PDEs
2015/16 TERM 1: MA4A2 Advanced PDEs

In Hanover, I taught the exercise courses including Global Analysis - Differential Geometry and Mathematics for Engineers I, II. The information is available here. [Hanover]

Current events:

Geometry of Manifolds. Simons Center for Geometry and Physics, USA, October 23-27, 2017.

Symplectic geometry - celebrating the work of Simon Donaldson. Cambridge, UK, August 14-18, 2017.

Pacific Rim Complex-Symplectic Geometry Conference. IBS Center for Geometry and Physics, Pohang, South Korea, July 31–August 4, 2017.

Differentialgeometrie im Großen. Oberwolfach, Germany, 2 July - 8 July 2017.

Preprints and Publications
  1. Construction of constant scalar curvature Kähler cone metrics (with J. Keller).
    ArXiv:1703.06312.

  2. Expansion formula for complex Monge–Ampère equation along cone singularities (with H. Yin).
    ArXiv:1609.03111.

  3. Uniqueness of constant scalar curvature Kähler metrics with cone singularities, I: Reductivity (with L. Li).
    ArXiv:1603.01743.

  4. Generalized Matsushima's theorem and Kähler-Einstein cone metrics (with L. Li).
    ArXiv:1511.02410.

  5. Regularity scales and convergence of the Calabi flow (with H. Z. Li and B. Wang).
    J. Geom. Anal. (2017) ArXiv:1501.01851.

  6. The geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics (with S. Calamai and D. Petrecca).
    New York J. Math. 22 (2016) 1111-1133. ArXiv:1405.1211.

  7. Geodesics in the space of Kähler cone metrics, I (with S. Calamai).
    Amer. J. Math. 137 (2015), no. 5. 1149-1208. ArXiv:1205.0056.

  8. I-properness of Mabuchi's K-energy.
    Calc. Var. Partial Differential Equations. 54 (2015), no. 3, 2807-2830. ArXiv:1410.1821.

  9. The Dirichlet and the weighted metrics for the space of Kähler metrics (with S. Calamai).
    Math. Ann. 363 (2015), no. 3, 817-856. ArXiv:1202.6610.

  10. Kähler metrics with cone singularities and uniqueness problem.
    Current trends in analysis and its applications, 395-408, Trends Math. Birkhäuser/Springer, Cham, 2015. [pdf]

  11. Kähler non-collapsing, eigenvalues and the Calabi flow (with H. Z. Li).
    J. Funct. Anal. 267 (2014), no. 5, 1593-1636. ArXiv:1309.4304.

  12. The pseudo-Calabi flow (with X. X. Chen).
    J. Reine Angew. Math. 674 (2013), 195-251. ArXiv:1004.2663.

  13. Stability of Calabi flow near an extremal metric (with H. N. Huang).
    Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 11 (2012), no. 1, 167-175. ArXiv:1007.4571.

  14. Stability of Kähler-Ricci flow in the space of Kähler metrics.
    Pacific J. Math. 251 (2011), no. 2, 469-497. ArXiv:1004.2695.