The conical complex Monge-Ampère equations on Kähler manifolds

Abstract

In this paper, by providing the uniform gradient estimates for a sequence of the approximating equations, we prove the existence, uniqueness and regularity of the conical parabolic complex Monge-Ampère equation with weak initial data. As an application, we prove a regularity estimates, that is, any $L^{\infty }$-solution of the conical complex Monge-Ampère equation admits the $C^{2,\alpha ,\beta }$-regularity.

arXiv admin note: text overlap with arXiv:1601.00060