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The first eigenvalue of the Laplacian on tori

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Publication:1159897
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DOI10.2748/tmj/1178229402zbMath0475.53038OpenAlexW2000966559MaRDI QIDQ1159897

Kazumi Tsukada

Publication date: 1981

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178229402

zbMATH Keywords

volumetorusthe first eigenvalue of the Laplacian


Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20)


Related Items

Upper bound for the second eigenvalue of a Schrödinger operator on a compact manifold and applications



Cites Work

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  • The first eigenvalue of the Laplacian on even dimensional spheres
  • On the least positive eigenvalue of Laplacian for compact homogeneous spaces
  • The first eigenvalue of the Laplacian on spheres
  • A construction of non-flat, compact irreducible Riemannian manifolds which are isospectral but not isometric
  • On the least positive eigenvalue of the Laplacian for compact group manifolds
  • The fundamental equations of a submersion
  • Totally geodesic maps
  • Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
  • On the least positive eigenvalue of the Laplacian for the compact quotient of a certain Riemannian symmetric space
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