# Dr Kai Zheng

Address:

Mathematics Institute

University of Warwick

Coventry CV4 7AL

United Kingdom

Room : B2.34

Tel: +44 (0) 24 7657 3512

E-Mail: K dot Zheng at warwick dot ac dot uk

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. My current **Research Interests** involve regularity/singularity phenomena of geometric PDEs, existence/uniqueness of critical metrics and convergence of geometric flows.

Here is my * Curriculum Vitae.* An almost list of my publications is available at arXiv and MathSciNet.

Co-organise:

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

**Travel/Visiting**

- Institut des Hautes Études Scientifiques, France, Sept.-Oct. 2018.
- Constant Scalar Curvature Metrics in Kähler and Sasaki Geometry. CIRM, France, January 15-19, 2018.
- Colloquia & Seminars. AMSS, Chinese Academy of Sciences, Beijing, December 4, 2017.
- Aarhus Differential Algebraic Geometry seminars. Centre for Quantum Geometry of Moduli Spaces, Denmark, November 7-8, 2017.
- Geometry of Manifolds. Simons Center for Geometry and Physics, USA, October 23-27, 2017.

**Teaching**

Teaching Responsibilities at Warwick:

2016/17 TERM 1: MA4A2 Advanced PDEs

2015/16 TERM 1: MA4A2 Advanced PDEs

At Hanover, I was a teaching assistant for

WS 2014/15, Mathematics for Engineers I

SS 2014, Mathematics for Engineers II

WS 2013/14, Mathematics for Engineers I

SS 2013, Mathematics for Engineers II

SS 2013, Global Analysis - Differential geometry

WS 2012/13, Mathematics for Engineers I

**Publications and Preprints**

**Stability of Kähler-Ricci flow in the space of Kähler metrics**

Pacific J. Math. 251 (2011), no. 2, 469-497.

ArXiv:1004.2695.**Stability of Calabi flow near an extremal metric**

Written in collaboration with H. N. Huang.

Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 11 (2012), no. 1, 167-175.

ArXiv:1007.4571.**The pseudo-Calabi flow**

Written in collaboration with X. X. Chen.

J. Reine Angew. Math. 674 (2013), 195-251.

ArXiv:1004.2663.**Kähler non-collapsing, eigenvalues and the Calabi flow**

Written in collaboration with H. Z. Li.

J. Funct. Anal. 267 (2014), no. 5, 1593-1636.

ArXiv:1309.4304.**Kähler metrics with cone singularities and uniqueness problem**

Current trends in analysis and its applications, 395-408, Trends Math. Birkhäuser/Springer, Cham, 2015.

Pdf File**The Dirichlet and the weighted metrics for the space of Kähler metrics**

Written in collaboration with S. Calamai.

Math. Ann. 363 (2015), no. 3, 817-856.

ArXiv:1202.6610.**I-properness of Mabuchi's K-energy**

Calc. Var. Partial Differential Equations. 54 (2015), no. 3, 2807-2830.

ArXiv:1410.1821.**Geodesics in the space of Kähler cone metrics, I**

Written in collaboration with S. Calamai.

Amer. J. Math. 137 (2015), no. 5. 1149-1208.

ArXiv:1205.0056.**The geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics**

Written in collaboration with S. Calamai and D. Petrecca.

New York J. Math. 22 (2016) 1111-1133.

ArXiv:1405.1211.**Regularity scales and convergence of the Calabi flow**

Written in collaboration with H. Z. Li and B. Wang.

J. Geom. Anal. (2017)

ArXiv:1501.01851. 52 pages.**Generalized Matsushima's theorem and Kähler-Einstein cone metrics**

Written in collaboration with L. Li.

Calc. Var. Partial Differential Equations. (2018).

ArXiv:1511.02410. 43 pages.**Uniqueness of constant scalar curvature Kähler metrics with cone singularities, I: Reductivity**

Written in collaboration with L. Li.

Math. Ann. (2017)

ArXiv:1603.01743. 40 pages.**Construction of constant scalar curvature Kähler cone metrics**

Written in collaboration with J. Keller.

Proc. Lond. Math. Soc. (2018).

ArXiv:1703.06312. 46 pages.**Expansion formula for complex Monge–Ampère equation along cone singularities**

Written in collaboration with H. Yin.

ArXiv:1609.03111. 29 pages.**Geodesics in the space of Kähler cone metrics, II. Uniqueness of constant scalar curvature Kähler cone metrics**

ArXiv:1709.09616. 71 pages.