Quasi-isometries and isoperimetric inequalities

Canton Pire, Alicia and Granados Sanandrés, Ana and Portilla Ferreira, Ana and Rodríguez García, José Manuel (2013). Quasi-isometries and isoperimetric inequalities. In: "XIV Encuentro de Análisis Real y Complejo (EARCO 2013)", 16/05/2013 - 18/05/2013, Teruel, España. pp..


Title: Quasi-isometries and isoperimetric inequalities
  • Canton Pire, Alicia
  • Granados Sanandrés, Ana
  • Portilla Ferreira, Ana
  • Rodríguez García, José Manuel
Item Type: Presentation at Congress or Conference (Other)
Event Title: XIV Encuentro de Análisis Real y Complejo (EARCO 2013)
Event Dates: 16/05/2013 - 18/05/2013
Event Location: Teruel, España
Title of Book: Resúmenes XIV Encuentro de Análisis Real y Complejo (EARCO 2013)
Date: 2013
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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We consider the stability of isoperimetric inequalities under quasi-isometries between Riemann surfaces. Kanai observed that quasi-isometries preserve isoperimetric inequalities on complete Riemannian manifolds with finite geometry: positive injectivity radius and Ricci curvature bounded from below (see [2]). In [1], it is shown that the linear isoperimetric inequality is a quasi-isometric invariant for planar Riemann surfaces (genus zero surfaces) with vanishing injectivity radius. Moreover, it is proved that non-linear isoperimetric inequalities can only hold for Riemann surfaces with positive injectivity radius, and hence, by Kanai's observation, preserved by quasi-isometries. In this talk we present an overview on isoperimetric inequalities and give some of the ideas of the proofs of the results cited above.

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Item ID: 33312
DC Identifier: http://oa.upm.es/33312/
OAI Identifier: oai:oa.upm.es:33312
Deposited by: Memoria Investigacion
Deposited on: 23 May 2015 08:52
Last Modified: 23 May 2015 08:52
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