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.
Funding source: National Key Research and Development Program of China
Award Identifier / Grant number: 2024YFA1014800
Award Identifier / Grant number: 2023YFA1009900
Funding source: National Natural Science Foundation of China
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
Funding source: Natural Science Foundation of Zhejiang Province
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.
References
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Covariant projective representations of Hilbert–Lie groups
- Solutions of the minimal surface equation and of the Monge–Ampère equation near infinity
- A Lindemann–Weierstrass theorem for 𝐸-functions
- Topology and dynamics of compact plane waves
- Diameter of Kähler currents
- CscK metrics near the canonical class
- On 3-nondegenerate CR manifolds in dimension 7 (I): The transitive case
- The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound
- Hodge–Tate stacks and non-abelian 𝑝-adic Hodge theory of v-perfect complexes on rigid spaces
Articles in the same Issue
- Frontmatter
- Covariant projective representations of Hilbert–Lie groups
- Solutions of the minimal surface equation and of the Monge–Ampère equation near infinity
- A Lindemann–Weierstrass theorem for 𝐸-functions
- Topology and dynamics of compact plane waves
- Diameter of Kähler currents
- CscK metrics near the canonical class
- On 3-nondegenerate CR manifolds in dimension 7 (I): The transitive case
- The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound
- Hodge–Tate stacks and non-abelian 𝑝-adic Hodge theory of v-perfect complexes on rigid spaces