Current Developments in Mathematics

Lectures on stability and constant scalar curvature

D.H. Phong and Jacob Sturm

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An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kähler metrics of constant scalar curvature. Besides classical notions such as Chow-Mumford stability, the emphasis is on several new stability conditions, such as K-stability, Donaldson’s infinite-dimensional GIT, and conditions on the closure of orbits of almost-complex structures under the diffeomorphism group. Related analytic methods are also discussed, including estimates for energy functionals, Tian-Yau-Zelditch approximations, estimates for moment maps, complex Monge-Amp`ere equations and pluripotential theory, and the Kähler-Ricci flow.

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Current Developments in Mathematics, Volume 2007 (2009), 101-176.

First available in Project Euclid: 5 October 2009

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Phong, D.H.; Sturm, Jacob. Lectures on stability and constant scalar curvature. Current Developments in Mathematics 2007 (2009), 101--176.

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