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An application of a $C^{2}$ $C^{2}$ -estimate for a complex Monge–Ampère equation

Hua Loo-Keng Center for Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China

E-mail Address: chang_li@pku.edu.cn

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Lei Ni

Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA

E-mail Address: leni@ucsd.edu

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, and

Xiaohua Zhu

School of Mathematical Science, Peking University, Beijing, P. R. China

E-mail Address: xhzhu@math.pku.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0129167X21400073Cited by:4 (Source: Crossref)

This article is part of the issue:

Special Issue in Honor of the 110th Anniversary of Late Professor S. S. Chern

Abstract

By studying a complex Monge–Ampère equation, we present an alternate proof to a recent result of Chu-Lee-Tam concerning the projectivity of a compact Kähler manifold $N^{n}$ $N^{n}$ with ${Ric}_{k} < 0$ ${Ric}_{k} < 0$ for some integer $k$ $k$ with $1 < k < n$ $1 < k < n$ , and the ampleness of the canonical line bundle $K_{N}$ $K_{N}$ .

Dedicated to the 110th anniversary of S. S. Chern with a great honor.

Keywords:

AMSC: 32Q10, 32Q15, 32W20, 53C55

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