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The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound

  • Jianchun Chu , Feng Wang and Kewei Zhang EMAIL logo
Published/Copyright: January 22, 2025

Abstract

In this work, optimal rigidity results for eigenvalues on Kähler manifolds with positive Ricci lower bound are established. More precisely, for those Kähler manifolds whose first eigenvalue agrees with the Ricci lower bound, we show that the complex projective space is the only one with the largest multiplicity of the first eigenvalue. Moreover, there is a specific gap between the largest and the second largest multiplicity. In the Kähler–Einstein case, almost rigidity results for eigenvalues are also obtained.

Award Identifier / Grant number: 2024YFA1014800

Award Identifier / Grant number: 2023YFA1009900

Award Identifier / Grant number: 12471052

Award Identifier / Grant number: 12271008

Award Identifier / Grant number: 12031017

Award Identifier / Grant number: 12101052

Award Identifier / Grant number: 12271040

Award Identifier / Grant number: 12271038

Award Identifier / Grant number: LR23A010001

Funding statement: J. Chu was partially supported by National Key R&D Program of China 2024YFA1014800 and 2023YFA1009900, NSFC grants 12471052 and 12271008, and the Fundamental Research Funds for the Central Universities, Peking University. F. Wang was partially supported by NSFC grant 12031017 and NSF of Zhejiang Province for Distinguished Young Scholars grant LR23A010001. K. Zhang was partially supported by NSFC grants 12101052, 12271040, and 12271038.

Acknowledgements

The authors thank Lifan Guan, Wenshuai Jiang and Jun Yu for helpful discussions.

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Received: 2024-02-23
Revised: 2024-09-15
Published Online: 2025-01-22
Published in Print: 2025-03-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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