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Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs

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URI: https://hdl.handle.net/10016/32615
ISSN: 0219-1997
DOI: https://doi.org/10.1142/S021919971750050X
UXXI: AR/0000021691
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cheeger_isoperimetric_CICM_2018_ps.pdf (823.43 KB)
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2018-08-01
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World Scientific Publishing
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Abstract
In this paper, we study the relationship of hyperbolicity and (Cheeger) isoperimetric inequality in the context of Riemannian manifolds and graphs. We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying this isoperimetric inequality, in terms of their Gromov boundary. Furthermore, we characterize the trees with isoperimetric inequality (without any hypothesis). As an application of our results, we obtain the solvability of the Dirichlet problem at infinity for these Riemannian manifolds and graphs, and that the Martin boundary is homeomorphic to the Gromov boundary.
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Gromov hyperbolicity, Cheeger isoperimetric constant, Bounded local geometry
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Martínez-Pérez, A., and Rodríguez, J. M. (2018). Cheeger isoperimetric constant of gromov hyperbolic manifolds and graphs. Communications in Contemporary Mathematics, 20(05), 1750050
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