Current Developments in Mathematics

Lectures on stability and constant scalar curvature

D.H. Phong and Jacob Sturm

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 5 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.cdm/1254748605

Mathematical Reviews number (MathSciNet)
MR2532997

Zentralblatt MATH identifier
1188.53081

Citation

Phong, D.H.; Sturm, Jacob. Lectures on stability and constant scalar curvature. Current Developments in Mathematics 2007 (2009), 101--176. https://projecteuclid.org/euclid.cdm/1254748605


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