Geodesic
Quantitative isoperimetric inequalities and homeomorphisms with finite distortion
Rajala, Kai1
1 University of Jyväskylä Department of Mathematics and Statistics P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 1, pp. 177-196

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We prove quantitative isoperimetric inequalities for images of the unit ball under homeomorphisms of exponentially integrable distortion. We show that the metric distortions of such domains can be controlled by their Fraenkel asymmetries. An application of the quantitative isoperimetric inequality proved by Hall and Fusco, Maggi, and Pratelli then shows that for these domains a version of Bonnesen’s inequality holds in all dimensions.

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Classification : 30C65, 46E35

Rajala, Kai 1

1 University of Jyväskylä Department of Mathematics and Statistics P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland 
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Rajala, Kai. Quantitative isoperimetric inequalities and homeomorphisms with finite distortion. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 1, pp. 177-196. http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_1_177_0/