Lectures on Stability and Constant Scalar Curvature

Details Lectures on Stability and Constant Scalar Curvature Lectures on Stability and Constant Scalar Curvature

2008-01-28

arxiv.org/abs/0801.4179v2

Mathematics

Differential Geometry

85 pages, minor corrections added

Scientific paper

An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler 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-Ampere equations and pluripotential theory, and the Kaehler-Ricci flow

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