RT Journal Article
T1 Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs
A1 Rodríguez García, José Manuel
A1 Martínez Pérez, Alvaro
AB 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.
PB World Scientific Publishing
SN 0219-1997
YR 2018
FD 2018-08-01
LK https://hdl.handle.net/10016/32615
UL https://hdl.handle.net/10016/32615
LA eng
NO Supported in part by a grant from Ministerio de Economíıa y Competitividad (MTM 2012-30719), Spain. Supported in part by two grants from Ministerio de Economíıa y Competitividad (MTM 2013-46374-P and MTM 2015- 69323-REDT), Spain, and a grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México.
DS e-Archivo
RD 27 jul. 2024