RT Journal Article
T1 Isoperimetric Inequalities in Riemann Surfaces and Graphs
A1 Martínez Pérez, Álvaro
A1 Rodríguez, José M.
AB A celebrated theorem of Kanai states that quasi-isometries preserve isoperimetric inequalities between uniform Riemannian manifolds (with positive injectivity radius) and graphs. Our main result states that we can study the (Cheeger) isoperimetric inequality in a Riemann surface by using a graph related to it, even if the surface has injectivity radius zero (this graph is inspired in Kanai’s graph, but it is different from it). We also present an application relating Gromov boundary and isoperimetric inequality.
PB Springer Nature Link
SN 1050-6926
SN 1559-002X
YR 2021
FD 2021
LK https://hdl.handle.net/20.500.14352/129071
UL https://hdl.handle.net/20.500.14352/129071
LA eng
NO Martínez-Pérez, Á., Rodríguez, J.M. Isoperimetric Inequalities in Riemann Surfaces and Graphs. J Geom Anal.2021; 31: 3583–3607.
NO Ministerio de Ciencia, Innovacion y Universidades
NO Ministerio de Economa y Competititvidad
NO Agencia Estatal de Investigacion
NO Fondo Europeo de Desarrollo Regional (FEDER)
DS Docta Complutense
RD 1 abr 2026