A sharp quantitative isoperimetric inequality in higher codimension
Verena Bögelein
Universität Salzburg, AustriaFrank Duzaar
Universität Erlangen-Nünberg, GermanyNicola Fusco
Università degli Studi di Napoli Federico II, Italy
![A sharp quantitative isoperimetric inequality in higher codimension cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rlm-volume-26-issue-3.png&w=3840&q=90)
Abstract
We establish a quantitative isoperimetric inequality in higher codimension. In particular, we prove that for any closed -dimensional manifold in the following inequality
holds true. Here, stands for the isoperimetric gap of , i.e. the deviation in measure of from being a round sphere and denotes a natural generalization of the Fraenkel asymmetry index of to higher codimensions.
Cite this article
Verena Bögelein, Frank Duzaar, Nicola Fusco, A sharp quantitative isoperimetric inequality in higher codimension. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 3, pp. 309–362
DOI 10.4171/RLM/709