Descripción
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We consider the stability of isoperimetric inequalities under quasi-isometries be- tween Riemann surfaces. Kanai observed that quasi-isometries preserve isoperimetric inequalities on complete Riemannian manifolds with finite geometry: positive injec- tivity 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 Rie- mann 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. | |
Internacional
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Si |
Nombre congreso
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XIV Encuentro de Ana ?lisis Real y Complejo, EARCO, 2013 |
Tipo de participación
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960 |
Lugar del congreso
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Teruel. España |
Revisores
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Si |
ISBN o ISSN
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0000000000000 |
DOI
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Fecha inicio congreso
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16/05/2013 |
Fecha fin congreso
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18/05/2013 |
Desde la página
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0 |
Hasta la página
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0 |
Título de las actas
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Resúmenes de comunicaciones a XIV Encuentro de Ana ?lisis Real y Complejo, EARCO, 2013 |