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Parabolic complex Monge–Ampère type equations on closed Hermitian manifolds

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Abstract

We study the parabolic complex Monge–Ampère type equations on closed Hermitian manifolds. We derive uniform \(C^\infty \) a priori estimates for normalized solutions, and then prove the \(C^\infty \) convergence. The result also yields a way to carry out the method of continuity for elliptic Monge–Ampère type equations.

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Acknowledgments

The author is very grateful to Bo Guan for constant support and countless advice. The main part of the work was done at the Ohio State University. The author also wishes to thank Ben Weinkove for his helpful suggestions and comments.

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  1. Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Wei Sun

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  1. Wei Sun
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Correspondence to Wei Sun.

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Communicated by F. H. Lin.

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Sun, W. Parabolic complex Monge–Ampère type equations on closed Hermitian manifolds. Calc. Var. 54, 3715–3733 (2015). https://doi.org/10.1007/s00526-015-0919-x

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