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

Published 29 May 2023 in math.CV | (2305.17955v1)

Abstract: We show the existence and uniqueness of bounded solutions to the degenerate complex Monge-Amp`ere 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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