Quantitative isoperimetric inequalities and homeomorphisms with finite distortion
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 1, p. 177-196

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.

Published online : 2018-06-21
Classification:  30C65,  46E35
@article{ASNSP_2012_5_11_1_177_0,
     author = {Rajala, Kai},
     title = {Quantitative isoperimetric inequalities and homeomorphisms with finite distortion},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {1},
     year = {2012},
     pages = {177-196},
     zbl = {1264.30016},
     mrnumber = {2953048},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2012_5_11_1_177_0}
}
Rajala, Kai. Quantitative isoperimetric inequalities and homeomorphisms with finite distortion. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 1, pp. 177-196. http://www.numdam.org/item/ASNSP_2012_5_11_1_177_0/

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