Lectures on Stability and Constant Scalar Curvature

2008/01/28 by D. H. Phong, Phong, D. H., Jacob Sturm +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0801.4179

openalex publication_date 2008/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Exponential estimates for plurisubharmonic functions and stochastic dynamics
• Extremal metrics on toric surfaces, I
• Energy Functionals for the Parabolic Monge-Ampere Equation
• CM Stability and the Generalized Futaki Invariant I
• A Compactness Property for Solutions of the Ricci Flow
• KÄHLER GEOMETRY OF TORIC VARIETIES AND EXTREMAL METRICS

Cited by

• Scalar Curvature and Stability of Toric Fibrations

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