On a uniform estimate for the quaternionic Calabi problem

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.

15 pages; the definition of quaternionic Hessian is replaced with the transposed matrix; other minor corrections

References in corpus (2)

• Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds
• Solvability of the quaternionic Monge-Ampere equation on compact manifolds with a flat hyperKaehler metric

Cited by in corpus (1)

• Solvability of the quaternionic Monge-Ampere equation on compact manifolds with a flat hyperKaehler metric