Extensions of a Bonnesen-style inequality to Minkowski spaces

Bonnesen-style Wulff isoperimetric inequality

The Wulff isoperimetric inequality is a natural extension of the classical isoperimetric inequality (Green and Osher in Asian J. Math. 3:659-676 1999). In this paper, we establish some Bonnesen-style Wulff isoperimetric inequalities and reverse Bonnesen-style Wulff isoperimetric inequalities. Those inequalities obtained are extensions of known Bonnesen-style inequalities and reverse Bonnesen-st...

Bonnesen-style inequality for the first eigenvalue on a complete surface of constant curvature

By Cheeger's isoperimetric constants, some lower bounds and upper bounds of [Formula: see text], the first eigenvalue on a complete surface of constant curvature, are given. Some Bonnesen-style inequalities and reverse Bonnesen-style inequalities for the first eigenvalue are obtained. Those Bonnesen-style inequalities obtained are stronger than the well-known Osserman's results and the upper bo...

Sharp Extensions of Bernstein’s Inequality to Rational Spaces

Sharp extensions of some classical polynomial inequalities of Bernstein are established for rational function spaces on the unit circle, on K := R (mod 2π), on [−1, 1] and on R. The key result is the establishment of the inequality

The Brunn-Minkowski-Type Inequality

The Stong Isoperimetric Inequality of Bonnesen

Simple means that the curve is assumed to have no self intersections. A circle of radius r has length L = 2πr and it encloses an area of A = πr = L 2 4π . Thus if γ is a simple closed curve of length L and encloses an area A, the isoperimetric inequality says that γ encloses an area no bigger than the area of the circle with the same length, or (I). The Isoperimetric inequality may be proved by...