Fully non-linear elliptic equations on compact hyperkähler manifolds

We consider a general class of elliptic equations on hypercomplex manifolds which includes the quaternionic Monge-Ampère equation, the quaternionic Hessian equation and the Monge-Ampère equation for quaternionic $$(n-1)$$ ( n - 1 ) -plurisubharmonic functions. We prove that under suitable assumptions the solutions to these equations on hyperkähler manifolds satisfy a C2,α C 2 , α a priori estimate.