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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Cheeger constant of simply connected, solvable Lie groups


Authors: Norbert Peyerimhoff and Evangelia Samiou
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1525-1529
MSC (2000): Primary 53C30, 22E25
Published electronically: December 23, 2003
MathSciNet review: 2053361
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Abstract: We show that the Cheeger isoperimetric constant of a solvable simply connected Lie group $G$ with Lie algebra $\mathfrak{G}$ is

\begin{displaymath}h(G)=\max_{H\in\mathfrak{G},\vert\vert H\vert\vert=1} {\rm tr\, }({\rm ad\, }(H)).\end{displaymath}


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Additional Information

Norbert Peyerimhoff
Affiliation: Mathematische Fakultät, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
Email: peyerim@math.ruhr-uni-bochum.de

Evangelia Samiou
Affiliation: Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
Email: samiou@ucy.ac.cy

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07404-5
PII: S 0002-9939(03)07404-5
Received by editor(s): November 6, 2001
Published electronically: December 23, 2003
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2003 American Mathematical Society