Isoperimetric inequalities in graphs and surfaces

Cantón Pire, Alicia and Granados, Ana and Portilla, Ana and Rodríguez, José M. (2014). Isoperimetric inequalities in graphs and surfaces. "Electronic Notes In Discrete Mathematics", v. 46 ; pp. 257-264. ISSN 1571-0653. https://doi.org/10.1016/j.endm.2014.08.034.

Description

Title: Isoperimetric inequalities in graphs and surfaces
Author/s:
  • Cantón Pire, Alicia
  • Granados, Ana
  • Portilla, Ana
  • Rodríguez, José M.
Item Type: Article
Título de Revista/Publicación: Electronic Notes In Discrete Mathematics
Date: September 2014
ISSN: 1571-0653
Volume: 46
Subjects:
Freetext Keywords: Isoperimetric inequality, linear isoperimetric inequality, quasi-isometry, infinite graphs, Riemann surfaces
Faculty: E.T.S.I. Navales (UPM)
Department: Matemática e Informática Aplicadas a la Ingenierías Civil y Naval
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Let M be the set of metric spaces that are either graphs with bounded degree or Riemannian manifolds with bounded geometry. Kanai proved the quasi-isometric stability of several geometric properties (in particular, of isoperimetric inequalities) for the spaces in M. Kanai proves directly these results for graphs with bounded degree; in order to prove the general case, he uses a graph (an ?-net) associated to a Riemannian manifold with bounded geometry. This paper studies the stability of isoperimetric inequalities under quasi-isometries between non-exceptional Riemann surfaces (endowed with their Poincare metrics). The present work proves the stability of the linear isoperimetric inequality for planar surfaces (genus zero surfaces) without the condition on bounded geometry. It is also shown the stability of any non-linear isoperimetric inequality.

More information

Item ID: 40203
DC Identifier: http://oa.upm.es/40203/
OAI Identifier: oai:oa.upm.es:40203
DOI: 10.1016/j.endm.2014.08.034
Official URL: http://www.sciencedirect.com/science/article/pii/S1571065314000353
Deposited by: Memoria Investigacion
Deposited on: 10 Jul 2017 09:02
Last Modified: 10 Jul 2017 09:02
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