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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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