On a uniform estimate for the quaternionic Calabi problem
  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. 
Semyon Alesker and Egor Shelukhin
math.CV math.AP