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The Cheeger constant of simply connected, solvable Lie groups
Authors:Norbert Peyerimhoff   Evangelia Samiou
Affiliation:Mathematische Fakultät, Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany ; Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
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_{Hinmathfrak{G},vertvert Hvertvert=1} {rm tr, }({rm ad, }(H)).end{displaymath}

Keywords:
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