On the essential spectrum of the Laplacian on complete manifolds

Hironori KUMURA

doi:10.2969/jmsj/04910001

Hironori KUMURA

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 1 Pages 1-14

DOI https://doi.org/10.2969/jmsj/04910001

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Published: 1997 Received: December 09, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Department of Mathematics Shizuoka University
2) Department of Mathematics Osaka University

Right :
1) Department of Mathematics Osaka University
2) Department of Mathematics Shizuoka University

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. Brooks, A relation between growth and the spectrum of the Laplacian, Math. Z., 178 (1981), 501-508.
2) R. Brooks, On the spectrum of non-compact manifolds with finite volume, Math. Z., 187 (1984), 425-432.
3) I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, New York, 1984. [4) J. F. Escobar, On the spectrum of the Laplacian on complete Riemannian manifolds, Comm. Partial Differential Equations, 11 (1986), 63-85.
5) J. F. Escobar and A. Freire, The spectrum of the Laplacian of manifolds of positive curvature, Duke Math. J., 65 (1992), 1-21.
6) H. Donnelly, On the essential spectrum of a complete Riemannian manifold, Topology, 20 (1981), 1-14.
7) H. Donnelly and N. Garofalo, Riemannian manifolds whose Laplacians have purely continuous spectrum, Math. Ann., 293 (1992), 143-161.
8) H. Donnelly and P. Li, Pure point spectrum and negative curvature for noncompact manifolds, Duke Math. J., 46 (1979), 497-503.
9) L. Karp, Noncompact manifolds with purely continuous spectrum, Michigan Math. J., 31 (1984), 339-347.
10) J. Li, Spectrum of the Laplacian on a complete Riemannian manifold with nonnegative Ricci curvature which possess(es) a pole, J. Math. Soc. Japan, 46 (1994), 213-216.
11) H. Urakawa, Spectra of Riemannian manifolds without focal points, in Geometry of Manifolds, (ed. K. Shiohama), Academic Press, 1989, pp. 435-443.

Right : [1] R. Brooks, A relation between growth and the spectrum of the Laplacian, Math. Z., 178 (1981), 501-508.
[2] R. Brooks, On the spectrum of non-compact manifolds with finite volume, Math. Z., 187 (1984), 425-432.
[3] I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, New York, 1984. [4) J. F. Escobar, On the spectrum of the Laplacian on complete Riemannian manifolds, Comm. Partial Differential Equations, 11 (1986), 63-85.
[4] J. F. Escobar, On the spectrum of the Laplacian on complete Riemannian manifolds, Comm. Partial Differential Equations, 11 (1986), 63-85.
[5] J. F. Escobar and A. Freire, The spectrum of the Laplacian of manifolds of positive curvature, Duke Math. J., 65 (1992), 1-21.
[6] H. Donnelly, On the essential spectrum of a complete Riemannian manifold, Topology, 20 (1981), 1-14.
[7] H. Donnelly and N. Garofalo, Riemannian manifolds whose Laplacians have purely continuous spectrum, Math. Ann., 293 (1992), 143-161.
[8] H. Donnelly and P. Li, Pure point spectrum and negative curvature for noncompact manifolds, Duke Math. J., 46 (1979), 497-503.
[9] L. Karp, Noncompact manifolds with purely continuous spectrum, Michigan Math. J., 31 (1984), 339-347.
[10] J. Li, Spectrum of the Laplacian on a complete Riemannian manifold with nonnegative Ricci curvature which possess(es) a pole, J. Math. Soc. Japan, 46 (1994), 213-216.
[11] H. Urakawa, Spectra of Riemannian manifolds without focal points, in Geometry of Manifolds, (ed. K. Shiohama), Academic Press, 1989, pp. 435-443.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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