On a uniform estimate for the quaternionic Calabi problem

Semyon Alesker; Egor Shelukhin

On a uniform estimate for the quaternionic Calabi problem

Complex Variables 2016-07-28 v3 Analysis of PDEs

Authors: Semyon Alesker , Egor Shelukhin

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.

Keywords

li-yau estimates and curvature calabi-yau manifold gradient estimates

Cite

@article{arxiv.1111.0403,
  title  = {On a uniform estimate for the quaternionic Calabi problem},
  author = {Semyon Alesker and Egor Shelukhin},
  journal= {arXiv preprint arXiv:1111.0403},
  year   = {2016}
}