The rigidity of eigenvalues on K\"ahler manifolds with positive Ricci lower bound
Differential Geometry
2024-12-24 v2
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.
Keywords
Cite
@article{arxiv.2401.15830,
title = {The rigidity of eigenvalues on K\"ahler manifolds with positive Ricci lower bound},
author = {Jianchun Chu and Feng Wang and Kewei Zhang},
journal= {arXiv preprint arXiv:2401.15830},
year = {2024}
}
Comments
v2, accepted version, to appear in Crelle