Kodai Mathematical Journal

A remark on exponential growth and the spectrum of the Laplacian

Yusuke Higuchi

Full-text: Open access

Abstract

In terms of the exponential growth of a non-compact Riemannian manifold, we give an upper bounds for the bottom of the essential spectrum of the Laplacian. This is an improvement of Brooks' result.

Article information

Source
Kodai Math. J. Volume 24, Number 1 (2001), 42-47.

Dates
First available in Project Euclid: 19 January 2005

Permanent link to this document
http://projecteuclid.org/euclid.kmj/1106157294

Digital Object Identifier
doi:10.2996/kmj/1106157294

Mathematical Reviews number (MathSciNet)
journal.issue.record/article MR1813717(2001m:58064)0987.5801610.2996/kmj/1106157294euclid.kmj/1106157294euclid.kmj/1106157294 20012005-01-19T00:00:00Z2005-01-19T00:00:00Z2011-09-23T07:33:51Z 2007-03-12T14:57:28Z Euclid Repository converted from existing (pre DPubS 2.0) data

Zentralblatt MATH identifier
0987.58016

Subjects
Primary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds

Citation

Higuchi, Yusuke. A remark on exponential growth and the spectrum of the Laplacian. Kodai Math. J. 24 (2001), no. 1, 42--47. doi:10.2996/kmj/1106157294. http://projecteuclid.org/euclid.kmj/1106157294.


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