Exact asymptotic rates for small Laplacian eigenvalues on degenerations of compact Kähler manifolds are derived, generalizing Dai-Yoshikawa to higher dimensions via Skoda inequality and auxiliary Monge-Ampère equations.
Phong, and Freid Tong,OnL ∞ estimates for complex Monge-Amp` ere equations, Annals of Mathematics198(2023), no
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Asymptotics of small eigenvalues on degenerations of K\"ahler manifolds
Exact asymptotic rates for small Laplacian eigenvalues on degenerations of compact Kähler manifolds are derived, generalizing Dai-Yoshikawa to higher dimensions via Skoda inequality and auxiliary Monge-Ampère equations.