Spectral geometry for certain noncompact Riemannian manifolds

DOI10.1007/BF01214913zbMath0432.58022WikidataQ115393866 ScholiaQ115393866MaRDI QIDQ1138835

Harold Donnelly

Publication date: 1979

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/172881

zbMATH Keywords

heat kernelpurely absolutely continuous spectrumspectrum of the Laplacianopen, complete, oriented Riemannian manifoldperturbation of the metric on a globally symmetric space of a noncompact type

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Differential geometry of symmetric spaces (53C35) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items

Cheeger-Müller theorem on manifolds with cusps, Spectral approximation by \(L_ 2\) discretization of the Laplace operator on manifolds of bounded geometry, Stability Theorems for the Continuous Spectrum of a Negatively Curved Manifold, EXISTENCE OF SPECTRAL GAPS, COVERING MANIFOLDS AND RESIDUALLY FINITE GROUPS, A GLUING FORMULA FOR THE ANALYTIC TORSION ON HYPERBOLIC MANIFOLDS WITH CUSPS, Relative index theory, The spectral asymptotics of elliptic operators of Schrödinger type on a hyperbolic space, Square integrable solutions of \(\Delta u+\lambda u=0\) on noncompact manifolds, MAPPING PROPERTIES OF HEAT KERNELS, MAXIMAL REGULARITY, AND SEMI-LINEAR PARABOLIC EQUATIONS ON NONCOMPACT MANIFOLDS, Brownian motion and random walks on manifolds

Cites Work

• Asymptotic expansions for the compact quotients of properly discontinuous group actions
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Integralrelationen Mathieuscher Funktionen. (Integral relation of Mathieu function)
• Scattering theory for differential operators. I: Operator theory
• Compact Clifford-Klein forms of symmetric spaces
• Spectral asymmetry and Riemannian Geometry. I
• Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item