The heat kernel and the spectrum of a class of nilmanifolds

DOI10.1080/03605309608821191zbMath0861.58035OpenAlexW2069184649MaRDI QIDQ4881611

Kenro Furutani

Publication date: 21 August 1996

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309608821191

zbMATH Keywords

integral representationspectrumheat kernelnilmanifolds

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Spectral theory; eigenvalue problems on manifolds (58C40)

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Determinant of Laplacians on Heisenberg manifolds. ⋮ Fundamental solution of a higher step Grushin type operator ⋮ Spectral zeta function of a sub-Laplacian on product sub-Riemannian manifolds and zeta-regularized determinant

Cites Work

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• The spectrum of the Laplacian on Riemannian Heisenberg manifolds
• A Poisson formula for Heisenberg manifolds
• On the Geometry of Groups of Heisenberg Type
• A lower bound for the heat kernel
• The spectrum of the laplacian on a certain nilpotent lie group
• Geometry of 2-Step Nilpotent Groups with a Left Invariant Metric. II

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