A sharp quantitative isoperimetric inequality in higher codimension

作者：Boegelein Verena; Duzaar Frank; Fusco Nicola

来源：Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 2015, 26(3): 309-362.

DOI：10.4171/RLM/709

• Isoperimetric inequality
• area minimizing currents
• stability

We establish a quantitative isoperimetric inequality in higher codimension. In particular, we prove that for any closed (n - 1)-dimensional manifold Gamma in Rn+k the following inequality
D(Gamma) >= cd(2)(Gamma)
holds true. Here, D(Gamma) stands for the isoperimetric gap of Gamma, i.e. the deviation in measure of Gamma from being a round sphere and d(Gamma) denotes a natural generalization of the Fraenkel asymmetry index of Gamma to higher codimensions.

• 出版日期2015