Geodesic
Spherical Mean and the Fundamental Group
Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 3-11

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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.
DOI : 10.4153/CMB-1991-001-2
Mots-clés : Spherical mean, geodesic random walk, amenable, transient, isoperimetric inequality, 58C40, 60J15 
Adachi, Toshiaki. Spherical Mean and the Fundamental Group. Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 3-11. doi: 10.4153/CMB-1991-001-2
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     title = {Spherical {Mean} and the {Fundamental} {Group}},
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     year = {1991},
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     doi = {10.4153/CMB-1991-001-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-001-2/}
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