Open Access
Translator Disclaimer
January, 2015 Quasi-isometries and isoperimetric inequalities in planar domains
Alicia CANTON, Ana GRANADOS, Ana PORTILLA, Jose M. RODRIGUEZ
J. Math. Soc. Japan 67(1): 127-157 (January, 2015). DOI: 10.2969/jmsj/06710127

Abstract

This paper studies the stability of isoperimetric inequalities under quasi-isometries between non-exceptional Riemann surfaces endowed with their Poincaré metrics. This stability was proved by Kanai in the more general setting of Riemannian manifolds under the condition of positive injectivity radius. The present work proves the stability of the linear isoperimetric inequality for planar surfaces (genus zero surfaces) without any condition on their injectivity radii. It is also shown the stability of any non-linear isoperimetric inequality.

Citation

Download Citation

Alicia CANTON. Ana GRANADOS. Ana PORTILLA. Jose M. RODRIGUEZ. "Quasi-isometries and isoperimetric inequalities in planar domains." J. Math. Soc. Japan 67 (1) 127 - 157, January, 2015. https://doi.org/10.2969/jmsj/06710127

Information

Published: January, 2015
First available in Project Euclid: 22 January 2015

zbMATH: 1311.30016
MathSciNet: MR3304016
Digital Object Identifier: 10.2969/jmsj/06710127

Subjects:
Primary: 30F45
Secondary: 30F20 , 31C12 , 53C20

Keywords: Isoperimetric inequality , linear isoperimetric inequality , Poincaré metric , quasi-isometry , Riemann surface

Rights: Copyright © 2015 Mathematical Society of Japan

JOURNAL ARTICLE
31 PAGES


SHARE
Vol.67 • No. 1 • January, 2015
Back to Top