Holder continuity of solutions to the complex Monge-Ampere equations on compact Kahler manifolds

Abstract

We study Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds. In [DNS] the authors have shown that the measure ${\omega }_u^n$ is moderate if $u$ is Hölder continuous. We prove a theorem which is a partial converse to this result.

Final version. To appear in Annales de l'Institut Fourier

References in corpus (2)

• Stability of Bounded Solutions for Degenerate Complex Monge-Ampère equations
• Convergence in capacity on compact Kähler manifolds