A uniform estimate for general quaternionic Calabi problem (with appendix by Daniel Barlet)

TL;DR

This paper establishes a uniform $C^0$ a priori estimate for solutions to the quaternionic Calabi problem on any compact HKT-manifold, extending previous results that required additional assumptions.

Contribution

It provides the first general $C^0$ estimate for the quaternionic Calabi problem without extra manifold restrictions.

Findings

Proves a $C^0$ a priori estimate for solutions on arbitrary compact HKT-manifolds.

Generalizes earlier results with additional assumptions.

Enhances understanding of quaternionic Monge-Ampère equations.

Abstract

We prove a $C^0$ a priori estimate on a solution of the quaternionic Calabi problem on an arbitrary compact connected HKT-manifold. This generalizes earlier works where this result was proven under certain extra assumptions on the manifold.