First eigenvalue estimates on complete Kähler manifolds

2025/07/12 by Wang, Mingwei, Yang, Xiaokui · 2 citations
#53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.09203

Abstract

Let (M,ω_g) be a complete Kähler manifold of complex dimension n. We prove that if the holomorphic sectional curvature satisfies HSC ≥ 2 , then the first eigenvalue λ₁ of the Laplacian on (M,ω_g) satisfies λ₁ ≥ (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.

Citations

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Cited by

• On diameter rigidity for Kähler manifolds with positive holomorphic sectional curvature
• First eigenvalue estimates on complete balanced Hermitian manifolds

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• Lower bounds for the first eigenvalue of the Laplacian on Kähler manifolds
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• A note on first eigenvalue estimates by coupling methods in Kähler and quaternion Kähler manifolds