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Journal of the European Mathematical Society

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Volume 17, Issue 2, 2015, pp. 259–271
DOI: 10.4171/JEMS/503

Published online: 2015-02-24

Cheeger inequalities for unbounded graph Laplacians

Frank Bauer[1], Matthias Keller[2] and Radosław K. Wojciechowski[3]

(1) Harvard University, Cambridge, USA
(2) The Hebrew University, Jerusalem, Israel
(3) York College of The City University of New York, Jamaica, USA

We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.

Keywords: Isoperimetric inequality, intrinsic metric, Schrödinger operators, weighted graphs, curvature, volume growth

Bauer Frank, Keller Matthias, Wojciechowski Radosław: Cheeger inequalities for unbounded graph Laplacians. J. Eur. Math. Soc. 17 (2015), 259-271. doi: 10.4171/JEMS/503