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|Title:||On the existence of extremal metrics||Authors:||Xu, X.||Issue Date:||Jun-1996||Citation:||Xu, X. (1996-06). On the existence of extremal metrics. Pacific Journal of Mathematics 174 (2) : 555-568. ScholarBank@NUS Repository.||Abstract:||We study the well known variational problem proposed by Calabi: Minimize the functional ∫M s2 gdvg among all metrics in a given Kahler class. We are able to establish the existence of the extremal when the closed Riemann surface has genus different from zero. We have also given a different proof of the result originally proved by Calabi that: On a closed Riemann surface, the extremal metric has constant scalar curvature on a closed Riemann surface, the extremal metric has constant scalar curvature, which originally is proved by Calabi.||Source Title:||Pacific Journal of Mathematics||URI:||http://scholarbank.nus.edu.sg/handle/10635/103795||ISSN:||00308730|
|Appears in Collections:||Staff Publications|
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