Families of Monge-Ampere measures with Holder continuous potentials

2017/08/31 by Vu, Duc-Viet
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.09595

Abstract

Let X be a compact Kahler manifold. Let F be a family of probability measures on X whose superpotentials are Holder continuous with uniform Holder exponent and Holder constant. We prove that the corresponding family of solutions of the complex Monge-Ampere equations whose right-hand sides are measures in F is Holder continuous.

Related

• Characterization of Monge-Ampere measures with Holder continuous potentials
• The complex Sobolev Space and Hölder continuous solutions to Monge-Ampère equations
• Hölder continuous potentials on manifolds with partially positive curvature
• Hölder continuous solutions of the Monge-Ampère equation on compact Hermitian manifolds
• Holder continuity of solutions to the complex Monge-Ampere equations on compact Kahler manifolds