The conical complex Monge-Ampère equations on Kähler manifolds

Published 13 Sep 2016 in math.AP | (1609.03821v1)

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-Amp`ere equation with weak initial data. As an application, we prove a regularity estimates, that is, any $L^{{\infty}$-solution} of the conical complex Monge-Amp`ere equation admits the $C^{{2,\alpha,\beta}$-regularity.}