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