A Sharp Quantitative Isoperimetric Inequality in Higher Codimension
نویسندگان
چکیده
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 Γ to higher codimensions.
منابع مشابه
Stability of the Steiner symmetrization of convex sets
The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.
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 کاملQuantitative Stability in the Isodiametric Inequality via the Isoperimetric Inequality
The isodiametric inequality is derived from the isoperimetric inequality trough a variational principle, establishing that balls maximize the perimeter among convex sets with fixed diameter. This principle brings also quantitative improvements to the isodiametric inequality, shown to be sharp by explicit nearly optimal sets.
متن کاملON THE ISOPERIMETRIC DEFICIT IN GAUSS SPACE By A. CIANCHI, N. FUSCO, F. MAGGI, and A. PRATELLI
We prove a sharp quantitative version of the isoperimetric inequality in the space Rn endowed with the Gaussian measure.
متن کاملOn the Isoperimetric Deficit in the Gauss Space
We find a sharp quantitative estimate for the isoperimetric inequality in R with the Gaussian measure.
متن کامل