On the constant scalar curvature Kähler metrics, apriori estimates

Abstract

In this paper, we derive apriori estimates for constant scalar curvature Kähler metrics on a compact Kähler manifold. We show that higher order derivatives can be estimated in terms of a $C^0$ bound for the Kähler potential. We also discuss some local versions of these estimates which can be of independent interest.

References in corpus (4)

• On deformation of extremal metrics
• On the existence of constant scalar curvature Kähler metric: a new perspective
• Approximation of weak geodesics and subharmonicity of Mabuchi energy
• A new complete Calabi-Yau metric on ${\mathbb{C}}^3$

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• Local curvature estimates along the $\kappa$-LYZ flow
• Mahler measures, Stable Pairs, and the Global coercive estimate for the Mabuchi Functional
• Convergence of cscK metrics on smooth minimal models of general type
• Faltings Heights, Igusa Local Zeta Functions, and the Stability Conjectures in Kahler Geometry I