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Spherical Mean and the Fundamental Group

Published online by Cambridge University Press:  20 November 2018

Toshiaki Adachi
Toshiaki Adachi*
Affiliation:
Kumamoto University, Kumamoto 860, Japan
*
Current address: Department of Mathematics, Nagoya Institute of Technology, Nagoya 466, Japan
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Abstract

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We investigate some properties of spherical means on the universal covering space of a compact Riemannian manifold. If the fundamental group is amenable then the greatest lower bounds of the spectrum of spherical Laplacians are equal to zero. If the fundamental group is nontransient so are geodesic random walks. We also give an isoperimetric inequality for spherical means.

Keywords

Spherical meangeodesic random walkamenabletransientisoperimetric inequality58C4060J15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 3 - 11
Copyright
Copyright © Canadian Mathematical Society 1991

Footnotes

Supported partially by Yukawa Foundation.

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