Heat invariants of Riemannian manifolds

DOI10.1007/BF02810670zbMath0996.58019arXivmath/9905073OpenAlexW2111948181WikidataQ115391561 ScholiaQ115391561MaRDI QIDQ1594896

Iosif Polterovich

Publication date: 4 November 2002

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9905073

zbMATH Keywords

heat kernelLaplacianKorteweg-de Vries hierarchyAgmon-Kannai method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

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Uses Software

• Mathematica

Cites Work

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• Compact isospectral sets of surfaces
• The spectral geometry of a Riemannian manifold
• From Agmon-Kannai expansion to Korteweg-de Vries hierarchy
• The volume of a small geodesic ball of a Riemannian manifold
• On the asymptotic behavior of spectral functions and resolvent kernels of elliptic operators
• Curvature and the eigenvalues of the Laplacian
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• On eigen-values of Laplacian and curvature of Riemannian manifold
• Leading Terms in the Heat Invariants
• Explicit formulae for the powers of a Schrödinger-like ordinary differential operator
• ASYMPTOTIC BEHAVIOUR OF THE RESOLVENT OF STURM-LIOUVILLE EQUATIONS AND THE ALGEBRA OF THE KORTEWEG-DE VRIES EQUATIONS
• A New Explicit Expression for the Korteweg - De Vries Hierarchy
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds