On The Quantitative Isoperimetric Inequality In The Plane

Abstract

In this paper we study the quantitative isoperimetric inequality in the plane. We prove the existence of a set $\Omega$, different from a ball, which minimizes the ratio $\delta (\Omega )/{\lambda }^2(\Omega )$, where $\delta$ is the isoperimetric deficit and $\lambda$ the Fraenkel asymmetry, giving a new proof ofthe quantitative isoperimetric inequality. Some new properties of the optimal set are also shown.

Equipe {é}quations aux d{é}riv{é}es partielles

Cited by in corpus (1)

• Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets