CFUC
Calabi flows with unbounded curvature
Total Cost €
0EC-Contrib. €
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Project "CFUC" data sheet
The following table provides information about the project.
| Coordinator |
THE UNIVERSITY OF WARWICK
Organization address contact info |
| Coordinator Country | United Kingdom [UK] |
| Project website | https://sites.google.com/site/drkaizheng/home |
| Total cost | 183˙454 € |
| EC max contribution | 183˙454 € (100%) |
| Programme |
1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility) |
| Code Call | H2020-MSCA-IF-2015 |
| Funding Scheme | MSCA-IF-EF-ST |
| Starting year | 2016 |
| Duration (year-month-day) | from 2016-05-26 to 2018-05-25 |
Partnership
Take a look of project's partnership.
| # | ||||
|---|---|---|---|---|
| 1 | THE UNIVERSITY OF WARWICK | UK (COVENTRY) | coordinator | 183˙454.00 |
Map
Project objective
In the 1950s, Calabi proposed a program in Kahler geometry and then introduced the Calabi flow, aiming to find the constant scalar curvature Kahler (cscK) metrics. When the first Chern class is zero, the cscK metric reduces to Ricci flat Kahler metric. The problem to find such metrics is called Calabi conjecture. Its resolution was Yau's Fields medal work. Generally, it is known as the Yau-Tian-Donaldson conjecture. Geometric flow provides an effective way to find canonical metrics. E.g., the theory by Hamilton and Perelman of Ricci flow has achieved great success to solve the conjecture of Poincare and Thurston, one of the seven $1 million Clay Mathematics Institute Millennium Prizes. X.X. Chen conjectured the Calab flow has long time existence. This proposal concerns singularity analysis of the Calabi flow, when the curvature gets unbounded.
Warwick leads a major new project funded by an EPSRC grant 'Singularities of Geometric PDEs', together with Imperial and Cambridge, making it a natural host for this proposal. The supervisor Topping is the Principal investigator of this project. He is a leading expert on geometric flows and nonlinear PDEs. He has considerable experience in supervising research: 14 postdocs and 8 PhD students. Currently, he is working on Ricci flows with unbounded curvature and presented an invited 45-minute lecture on this topic at Seoul ICM in 2014.
Zheng completed his PhD at the Chinese Academic of Sciences under the supervision of W.Y. Ding and X.X. Chen. From his advisors, Zheng gained intimate understanding of Kahler geometry. He worked as a postdoc at the Institut Fourier in France and then Leibniz Universitaet in Germany. Up to May 2015, his research experience has entirely been outside UK. He is ambitious to establish himself as an independent researcher at a prestigious UK institution. He has published 8 papers in high reputation international journals. This project will help him to integrate himself into the UK research system.
Publications
| year | authors and title | journal | last update |
|---|---|---|---|
| 2018 |
Li, Long; Wang, Jian; Zheng, Kai Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors published pages: , ISSN: , DOI: |
2019-06-13 | |
| 2016 |
Yin, Hao; Zheng, Kai Expansion formula for complex Monge-Amp`ere equation along cone singularities published pages: , ISSN: , DOI: |
2019-06-13 | |
| 2018 |
Julien Keller, Kai Zheng Construction of constant scalar curvature Kähler cone metrics published pages: 527-573, ISSN: 0024-6115, DOI: 10.1112/plms.12132 |
Proceedings of the London Mathematical Society 117/3 | 2019-06-13 |
| 2017 |
Long Li, Kai Zheng Uniqueness of constant scalar curvature Kähler metrics with cone singularities. I: reductivity published pages: , ISSN: 0025-5831, DOI: 10.1007/s00208-017-1626-z |
Mathematische Annalen | 2019-06-13 |
| 2018 |
Haozhao Li, Bing Wang, Kai Zheng Regularity Scales and Convergence of the Calabi Flow published pages: 2050-2101, ISSN: 1050-6926, DOI: 10.1007/s12220-017-9896-y |
The Journal of Geometric Analysis 28/3 | 2019-06-13 |
| 2018 |
Zheng, Kai Existence of constant scalar curvature Kaehler cone metrics, properness and geodesic stability published pages: , ISSN: , DOI: |
2019-06-13 | |
| 2018 |
Long Li, Kai Zheng Generalized Matsushima’s theorem and Kähler–Einstein cone metrics published pages: , ISSN: 0944-2669, DOI: 10.1007/s00526-018-1313-2 |
Calculus of Variations and Partial Differential Equations 57/2 | 2019-06-13 |
| 2018 |
Zheng, Kai Geodesics in the space of Kahler cone metrics, II. Uniqueness of constant scalar curvature Kahler cone metrics published pages: , ISSN: 0010-3640, DOI: |
Communications on Pure and Applied Mathematics | 2019-06-13 |
| 2016 |
Calamai, Simone; Petrecca, David; Zheng, Kai On the geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics. published pages: 1111-1133, ISSN: 1076-9803, DOI: |
New York Journal of Mathematics Volume 22 | 2019-06-13 |
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