On a uniform estimate for the quaternionic Calabi problem

TL;DR

This paper proves a uniform bound for solutions to the quaternionic Calabi-Yau equation on compact HKT manifolds, introducing a quaternionic Gauduchon theorem as a key step.

Contribution

It establishes a C^0 a priori estimate for the quaternionic Calabi-Yau equation and develops a quaternionic analogue of the Gauduchon theorem.

Findings

Established a C^0 bound for solutions on compact HKT manifolds

Proved a quaternionic version of the Gauduchon theorem

Extended techniques from complex geometry to quaternionic setting

Abstract

We establish a C^0 a priori bound on the solutions of the quaternionic Calabi-Yau equation (of Monge-Ampere type) on compact HKT manifolds with a locally flat hypercomplex structure. As an intermediate step, we prove a quaternionic version of the Gauduchon theorem.