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Transactions of the American Mathematical Society

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Integral inequalities for holomorphic maps and applications


Author: Yashan Zhang
Journal: Trans. Amer. Math. Soc. 374 (2021), 2341-2358
MSC (2020): Primary 53C55
DOI: https://doi.org/10.1090/tran/8293
Published electronically: January 21, 2021
MathSciNet review: 4223018
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Abstract: We derive some integral inequalities for holomorphic maps between complex manifolds. As applications, some rigidity and degeneracy theorems for holomorphic maps without assuming any pointwise curvature signs for both the domain and target manifolds are proved, in which key roles are played by total integration of the function of the first eigenvalue of second Ricci curvature and an almost nonpositivity notion for holomorphic sectional curvature introduced in our previous work. We also apply these integral inequalities to discuss the infinite-time singularity type of the Kähler-Ricci flow. The equality case is characterized for some special settings.


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Additional Information

Yashan Zhang
Affiliation: School of Mathematics and Hunan Province Key Lab of Intelligent Information Processing and Applied Mathematics, Hunan University, Changsha 410082, People’s Republic of China
MR Author ID: 1234610
Email: yashanzh@hnu.edu.cn

Keywords: Holomorphic maps, integral inequality, first eigenvalue of second Ricci curvature, almost nonpositive holomorphic sectional curvature, rigidity theorem, degeneracy theorem, Kähler-Ricci flow.
Received by editor(s): November 1, 2019
Received by editor(s) in revised form: August 11, 2020
Published electronically: January 21, 2021
Additional Notes: The author was partially supported by Fundamental Research Funds for the Central Universities (No. 531118010468) and National Natural Science Foundation of China (No. 12001179)
Article copyright: © Copyright 2021 American Mathematical Society