On complete Kähler manifolds with HSC ≥ 2, the first eigenvalue of the Laplacian is at least (320n+256)/(81n+63), which tends to 320/81 as n grows.
Conjugate radius, volume comparison and rigidity
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abstract
In this paper, we prove conjugate radius estimate, volume comparison and rigidity theorems for K\"ahler manifolds with various curvature conditions.
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math.DG 1years
2025 1verdicts
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First eigenvalue estimates on complete K\"ahler manifolds
On complete Kähler manifolds with HSC ≥ 2, the first eigenvalue of the Laplacian is at least (320n+256)/(81n+63), which tends to 320/81 as n grows.