Constant scalar curvature Kähler metric and K-energy

Constant Scalar Curvature Kähler Metric Obtains the Minimum of K-energy

K-stability of constant scalar curvature Kähler manifolds

We show that a polarised manifold with a constant scalar curvature Kähler metric and discrete automorphisms is K-stable. This refines the K-semistability proved by S. K. Donaldson.

Blowing up Kähler manifolds withconstant scalar curvature, II

In this paper we prove the existence of Kähler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold which already carries a Kähler constant scalar curvature metric. Necessary conditions of the number and locations of the blow up points are given. 1991 Math. Subject Classification: 58E11, 32C17.

The Space of Kähler metrics

Donaldson conjectured[14] that the space of Kähler metrics is geodesic convex by smooth geodesic and that it is a metric space. Following Donaldson’s program, we verify the second part of Donaldson’s conjecture completely and verify his first part partially. We also prove that the constant scalar curvature metric is unique in each Kähler class if the first Chern class is either strictly negativ...

Polarized 4-Manifolds, Extremal Kähler Metrics, and Seiberg-Witten Theory

Using Seiberg-Witten theory, it is shown that any Kähler metric of constant negative scalar curvature on a compact 4-manifold M minimizes the L-norm of scalar curvature among Riemannian metrics compatible with a fixed decomposition H(M) = H ⊕ H−. This implies, for example, that any such metric on a minimal ruled surface must be locally symmetric.