We establish a quantitative isoperimetric inequality in higher codimension. In particular, we prove that for any closed (n-1)-dimensional manifold \Gamma in \R^{n+k} the following inequality $$D(\Gamma)\ge C d^2(\Gamma)$$ 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 codimension.
On the stability of Almgren's isoperimetric inequality / Fusco, Nicola. - (2013). (Intervento presentato al convegno Calcul des Variations et Équations Différentielles tenutosi a Lausanne nel 10-12 giugno 2013).
On the stability of Almgren's isoperimetric inequality
FUSCO, NICOLA
2013
Abstract
We establish a quantitative isoperimetric inequality in higher codimension. In particular, we prove that for any closed (n-1)-dimensional manifold \Gamma in \R^{n+k} the following inequality $$D(\Gamma)\ge C d^2(\Gamma)$$ 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 codimension.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
