The Cheeger constant of simply connected, solvable Lie groups
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- by Norbert Peyerimhoff and Evangelia Samiou
- Proc. Amer. Math. Soc. 132 (2004), 1525-1529
- DOI: https://doi.org/10.1090/S0002-9939-03-07404-5
- Published electronically: December 23, 2003
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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 \[ h(G)=\max _{H\in \mathfrak {G},||H||=1} \textrm {tr }(\textrm {ad }(H)).\]References
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Bibliographic Information
- Norbert Peyerimhoff
- Affiliation: Mathematische Fakultät, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
- MR Author ID: 290247
- 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
- Received by editor(s): November 6, 2001
- Published electronically: December 23, 2003
- Communicated by: Wolfgang Ziller
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1525-1529
- MSC (2000): Primary 53C30, 22E25
- DOI: https://doi.org/10.1090/S0002-9939-03-07404-5
- MathSciNet review: 2053361