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arXiv · 1609.03821

The conical complex Monge-Ampère equations on Kähler manifolds

Jiawei Liu·Chuanjing Zhang
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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 $C^{2,α,β}$-regularity.

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Jiawei Liu, Chuanjing Zhang. 2016-09-13. The conical complex Monge-Ampère equations on Kähler manifolds. https://arxiv.org/abs/1609.03821

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