Fraenkel Asymmetry
نویسنده
چکیده
For simplicity, we restrict attention to subregions of the plane. Let Ω ⊆ R 2 be the closure of a bounded, open, connected set of area |Ω| with piecewise continuously differentiable boundary and perimeter . The classical isoperimetric inequality:
منابع مشابه
A Strong Form of the Quantitative Isoperimetric Inequality
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.
متن کاملA Sharp Quantitative Isoperimetric Inequality in Higher Codimension
We establish a quantitative isoperimetric inequality in higher codimension. In particular, we prove that for any closed (n − 1)-dimensional manifold Γ in Rn+k the following inequality D(Γ) ≥ Cd(Γ) holds true. Here, D(Γ) stands for the isoperimetric gap of Γ, i.e. the deviation in measure of Γ from being a round sphere and d(Γ) denotes a natural generalization of the Fraenkel asymmetry index of ...
متن کاملA 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 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 کاملThe disjunction and related properties for constructive Zermelo-Fraenkel set theory
This paper proves that the disjunction property, the numerical existence property, Church’s rule, and several other metamathematical properties hold true for Constructive Zermelo-Fraenkel Set Theory, CZF, and also for the theory CZF augmented by the Regular Extension Axiom. As regards the proof technique, it features a self-validating semantics for CZF that combines realizability for extensiona...
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 2014