On deformation of extremal metrics

Abstract

We generalize the bifurcation technique of Bando-Mabuchi in the context of extremal metrics.

arXiv commentReferences added

References in corpus (3)

• On the existence of constant scalar curvature Kähler metric: a new perspective
• Approximation of weak geodesics and subharmonicity of Mabuchi energy
• Convexity of the K-energy on the space of Kahler metrics and uniqueness of extremal metrics

Cited by in corpus (14)

• On the constant scalar curvature Kähler metrics, existence results
• On the constant scalar curvature Kähler metrics, general automorphism group
• On the constant scalar curvature Kähler metrics, apriori estimates
• On the existence of constant scalar curvature Kähler metric: a new perspective
• Weighted K-stability of polarized varieties and extremality of Sasaki manifolds
• Deformations from a given Kähler metric to a twisted cscK metric
• Weighted K-stability and coercivity with applications to extremal Kahler and Sasaki metrics
• Monge-Ampère operators, energy functionals, and uniqueness of Sasaki-extremal metrics
• Scalar curvature and properness on Sasaki manifolds
• Geometrical pluripotential theory on Sasaki manifolds
• On Calabi's extremal metric and properness
• Geodesic Convexity of Small Neighborhood in the Space of Kähler Potentials
• Approximation of weak geodesics and subharmonicity of Mabuchi energy, II: $\epsilon$-geodesics
• Strict convexity of the Mabuchi functional for energy minimizers