H\"older continuous potentials on manifolds with partially positive curvature

TL;DR

This paper proves that solutions to the complex Monge-Ampère equation on certain Kähler manifolds are uniformly H"older continuous when the manifold has non-negative orthogonal bisectional curvature and the right-hand side is in L^p for p>1.

Contribution

It establishes H"older continuity of solutions under geometric curvature conditions and integrability assumptions, extending regularity results in complex geometry.

Findings

Solutions are uniformly H"older continuous under specified conditions.

The result applies to manifolds with non-negative orthogonal bisectional curvature.

The regularity holds for right-hand sides in L^p, p>1.

Abstract

It is proved that solutions of the complex Monge-Amp\`ere equation on compact K\"ahler manifolds with right hand side in $L^p, p>1$ are uniformly H\"older continuous under the assumption on non-negative orthogonal bisectional curvature.