Open Access
VOL. 2007 | 2009 Lectures on stability and constant scalar curvature
D.H. Phong, Jacob Sturm

Editor(s) David Jerison, Barry Mazur, Tomasz Mrowka, Wilfried Schmid, Richard P. Stanley, Shing-Tung Yau

Current Developments in Mathematics, 2009: 101-176 (2009)


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-Ampère equations and pluripotential theory, and the Kähler-Ricci flow.


Published: 1 April 2009
First available in Project Euclid: 5 October 2009

zbMATH: 1188.53081
MathSciNet: MR2532997

Rights: Copyright © 2009 International Press of Boston

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