On the constant scalar curvature Kähler metrics (I)—A priori estimates
Xiuxiong Chen, Jingrui Cheng
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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript 0"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">C^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> bound for the Kähler potential.
Topics & Concepts
Scalar curvatureMathematicsManifold (fluid mechanics)CurvatureScalar (mathematics)A priori and a posterioriAlgorithmKähler manifoldMathematical analysisGeometryPhilosophyEpistemologyEngineeringMechanical engineeringGeometry and complex manifoldsGeometric Analysis and Curvature FlowsAlgebraic Geometry and Number Theory