A Strong Form of the Quantitative Isoperimetric Inequality
نویسندگان
چکیده
We give a refinement of the quantitative isoperimetric inequality. We prove that the isoperimetric gap controls not only the Fraenkel asymmetry but also the oscillation of the boundary.
منابع مشابه
A Strong Form of the Quantitative Wulff Inequality
Quantitative isoperimetric inequalities are shown for anisotropic surface energies where the isoperimetric deficit controls both the Fraenkel asymmetry and a measure of the oscillation of the boundary with respect to the boundary of the corresponding Wulff shape.
متن کاملA Quantitative Isoperimetric Inequality for Fractional Perimeters
Recently Frank & Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here in a quantitative form.
متن کاملOn the quantitative isoperimetric inequality in the plane
In this paper we study the quantitative isoperimetric inequality in the plane. We prove the existence of a set Ω, different from a ball, which minimizes the ratio δ(Ω)/λ(Ω), where δ is the isoperimetric deficit and λ the Fraenkel asymmetry, giving a new proof of the quantitative isoperimetric inequality. Some new properties of the optimal set are also shown.
متن کاملA Quantitative Isoperimetric Inequality on the Sphere
In this paper we prove a quantitative version of the isoperimetric inequality on the sphere with a constant independent of the volume of the set E.
متن کاملA Mass Transportation Approach to Quantitative Isoperimetric Inequalities
A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially Gromov’s proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski inequality for...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011