Degeneration of algebraic manifolds and the spectrum of Laplacian

DOI10.1017/S002776300000622XzbMath0880.58030OpenAlexW1677228031MaRDI QIDQ4352117

Ken-Ichi Yoshikawa

Publication date: 8 February 1998

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s002776300000622x

zbMATH Keywords

spectrumLaplacianprojective algebraic manifolds

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Elliptic equations on manifolds, general theory (58J05) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (11)

Convergence of Riemannian manifolds and Laplace operators. I ⋮ Spectral convergence of Riemannian manifolds. II ⋮ Singular Gauduchon metrics ⋮ Spectral convergence of conformally immmersed surfaces with bounded mean curvature ⋮ Variation of singular Kähler-Einstein metrics: Kodaira dimension zero (with an appendix by Valentino Tosatti) ⋮ Convergence of Calabi-Yau manifolds ⋮ Sobolev spaces and Bochner Laplacian on complex projective varieties and stratified pseudomanifolds ⋮ \(q\)-parabolicity of stratified pseudomanifolds and other singular spaces ⋮ Sobolev spaces on quasi-Kähler complex varieties ⋮ Bounds for Laplace eigenvalues of Kähler metrics ⋮ On the Laplace–Beltrami operator on compact complex spaces

Cites Work

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• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Heat kernel estimates and lower bound of eigenvalues
• Spectral convergence on degenerating surfaces
• Spectral geometry of semi-algebraic sets
• Degeneration of Kähler manifolds
• Spectra of domains in compact manifolds
• Closedness of the Douady spaces of compact Kähler spaces
• Spectral convergence of Riemannian manifolds
• On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth
• Spectral convergence of Riemannian manifolds. II
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Heat Equations on Minimal Submanifolds and Their Applications

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