We establish the validity of a quantitative isoperimetric inequality in higher codimension. To be precise we show for any closed (n-1)-dimensional manifold Γ in R^{n+k} that the quantitative isoperimetric inequality D(Γ)≥ C_1 d^2(Γ) holds true. Here D(Γ) stands for the isoperimetric deficit of Γ, i.e., the deviation in measure of Γ being a round sphere. Further, d(Γ ) denotes a natural generalization to higher codimension of the Fraenkel asymmetry index of Γ.
A sharp quantitative isoperimetric inequality in higher codimension / V., Bögelein; F., Duzaar; Fusco, Nicola. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1720-0768. - 26:(2015), pp. 309-362. [10.4171/RLM/709]
A sharp quantitative isoperimetric inequality in higher codimension
FUSCO, NICOLA
2015
Abstract
We establish the validity of a quantitative isoperimetric inequality in higher codimension. To be precise we show for any closed (n-1)-dimensional manifold Γ in R^{n+k} that the quantitative isoperimetric inequality D(Γ)≥ C_1 d^2(Γ) holds true. Here D(Γ) stands for the isoperimetric deficit of Γ, i.e., the deviation in measure of Γ being a round sphere. Further, d(Γ ) denotes a natural generalization to higher codimension of the Fraenkel asymmetry index of Γ.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
