2026-06-27T16:05:49Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/1290712025-12-17T01:03:18Zcom_20.500.14352_14col_20.500.14352_15

Martínez Pérez, Álvaro Rodríguez, José M. 2025-12-16T09:21:51Z 2025-12-16T09:21:51Z 2021 Martínez-Pérez, Á., Rodríguez, J.M. Isoperimetric Inequalities in Riemann Surfaces and Graphs. J Geom Anal.2021; 31: 3583–3607. 1050-6926 1559-002X 10.1007/s12220-020-00407-0 https://hdl.handle.net/20.500.14352/129071 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. eng open access Isoperimetric Inequalities in Riemann Surfaces and Graphs journal article