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arXiv · 2401.15830

The rigidity of eigenvalues on K\"ahler manifolds with positive Ricci lower bound

Jianchun Chu·Feng Wang·Kewei Zhang
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Abstract

In this work, optimal rigidity results for eigenvalues on K\"ahler manifolds with positive Ricci lower bound are established. More precisely, for those K\"ahler 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 K\"ahler--Einstein case, almost rigidity results for eigenvalues are also obtained.

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Jianchun Chu, Feng Wang, Kewei Zhang. 2024-01-29. The rigidity of eigenvalues on K\"ahler manifolds with positive Ricci lower bound. https://arxiv.org/abs/2401.15830

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