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- Title
Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs.
- Authors
Martínez-Pérez, Alvaro; Rodríguez, José M.
- 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.
- Subjects
HYPERBOLIC geometry; MANIFOLDS (Mathematics); MATHEMATICAL inequalities; MATHEMATICAL bounds; DIRICHLET problem; GRAPH theory
- Publication
Communications in Contemporary Mathematics, 2018, Vol 20, Issue 5, pN.PAG
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S021919971750050X