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arXiv · 2507.09203

First eigenvalue estimates on complete K\"ahler manifolds

Mingwei Wang·Xiaokui Yang
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Abstract

Let $ (M,\omega_g) $ be a complete K\"ahler manifold of complex dimension $n$. We prove that if the holomorphic sectional curvature satisfies $\mathrm{HSC} \geq 2 $, then the first eigenvalue $\lambda_1$ of the Laplacian on $(M,\omega_g)$ satisfies $$ \lambda_1 \geq \frac{320(n-1)+576}{81(n-1)+144}.$$ This result is established through a new Bochner-Kodaira type identity specifically developed for holomorphic sectional curvature.

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Mingwei Wang, Xiaokui Yang. 2025-07-12. First eigenvalue estimates on complete K\"ahler manifolds. https://arxiv.org/abs/2507.09203

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