Degenerate complex Monge-Amp\` ere type equations on compact Hermitian manifolds and applications

2023/05/29 by Li, Yinji, Wang, Zhiwei, Zhou, Xiangyu · 3 citations
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.17955

Abstract

We show the existence and uniqueness of bounded solutions to the degenerate complex Monge-Ampère type equations on compact Hermitian manifolds. We also study the asymptotics of these solutions. As applications, we give partial answers to the Tosatti-Weinkove conjecture and Demailly-P\u aun conjecture.

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• Mixed Hessian inequalities on Hermitian manifolds and applications
• Monge-Ampère equations with prescribed singularities on compact Hermitian manifolds
• Degenerate complex Monge-Ampère type equations on compact Hermitian manifolds and applications II

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