听Constant scalar curvature Kahler metrics and properness theorem
听Constant scalar curvature Kahler metrics and properness theorem
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Jingrui Cheng, Stony Brook University
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Constant scalar curvature Kahler metric(cscK) is a natural higher dimensional generalization of the听constant curvature metric on Riemann surfaces. One of the main difficulties in understanding the existence of听cscK metric is the complexity of the underlying partial differential equation. We take up this challenge and听show that the existence of cscK metric on compact Kahler manifold is equivalent to the properness of听Mabuchi energy (whose critical point are cscK metrics). I will also discuss future problems if time permits.听
This is based on joint work with Xiuxiong Chen.
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