A standard Bonnesen inequality states that what I call the Bonnesen function (0.1) B(r) = rL - A - nr2 is positive for all r G [rin, r J , where rin , the inradius, is the radius of one of the largest inscribed circles while the outradius rout is the radius of the smallest circumscribed circle.

A standard Bonnesen inequality states that what I call the Bonnesen function (0.1) B (r) = rL - A - nr2 is positive for all r G [rin, r J, where rin, the inradius, is the radius of one of the

From Property 2, it follows that equality can hold in (1) only when C is a circle. The effect of Property 3 is to give a measure of the curve's "deviation from circularity." Our purpose here is, first, to review what is known for plane domains. In particular, we include ten different inequalities of the In this paper, we obtain some Bonnesen-style Minkowski inequalities of mixed volumes of convex bodies K and L in the Euclidean space Rn. Let L be the unit ball; we get some better Bonnesen-style isoperimetric inequalities than Dinghas’s result for n≥3. Bonnesen's inequality is an inequality relating the length, the area, the radius of the incircle and the radius of the circumcircle of a Jordan curve. It is a strengthening of the classical isoperimetric inequality. More precisely, consider a planar simple closed curve of length bounding a domain of area . Some New Bonnesen-style inequalities.

For a simple closed curve γ, the stronger inequality due to Bonnesen holds: L 2 − 4 π A ≥ π 2 ( R o u t − R i n) 2 , where, setting Ω = Int ( γ) , R i n and R o u t denote the inner and outer radii of the sets: The purpose of this paper is to find a new Bonnesen-style inequality with equality condition on surfaces \(\mathbb{X}_{\kappa}\) of constant curvature, especially on the hyperbolic plane \(\mathbb{H}^{2}\) by integral geometric method. We are going to seek the following Bonnesen-style inequality for a convex set K in \(\mathbb{X}_{\kappa}\): A standard Bonnesen inequality states that what I call the Bonnesen function (0.1) B(r) = rL - A - nr2 is positive for all r G [rin, r J , where rin , the inradius, is the radius of one of the largest inscribed circles while the outradius rout is the radius of the smallest circumscribed circle. Bonnesen-style inequalities hold true in Rn under the John domain assumption which rules out cusps. Our main tool is a proof of the isoperimetric inequality for symmetric domains which gives an explicit estimate for the isoperimetric deﬁcit. We use the sharp quantitative inequalities proved in Fusco et al. (2008) [7] and Bonnesen's inequality: | |Bonnesen's inequality| is an |inequality| relating the length, the area, the radius of t World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. We first estimate the containment measure of a convex domain to contain in another in a surface \mathbb {X}_\varepsilon of constant curvature ε.

We prove an inequality of Bonnesen type for the real projective plane, generalizing Pu’s systolic inequality for positively-curved metrics. The remainder term in the inequality, analogous to that in Bonnesen’s inequality…

Some New Bonnesen-style inequalities. J Korean Math Soc, 2011, 48: 421-430.

Others may be found in a recent paper of the author [4] on Bonnesen inequalities and in the book of. Santaló [4] on integral geometry and geometric probability. An

(Minkler and Fadem Hummert, M. L., Garstka, T. A., Ryan, E. B., Bonnesen, J. L.. (2004).

The limiting case as κ → 0 in either of Theorems 2.1 and 3.3 yields the classical Bonnesen inequality (1), as described above. A brief and direct proof of (1) using kinematic arguments, also described in [San76], is presented at the close of English: llustration of Bonnesen inequality (2) Français : Illustration de l'inégalité de Bonnesen, pour le théorème isopérimétrique en dimension 2. Première figure pour la démonstration. We consider the positive centre sets of regular n-gons, rectangles and half discs, and conjecture a Bonnesen type inequality concerning positive centre sets Bonnesen type inequalities.
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Inequalities & Applications Volume 11, Number 4 (2008), 739–748 EXTENSIONS OF A BONNESEN–STYLE INEQUALITY TO MINKOWSKI SPACES HORST MARTINI AND ZOKHRAB MUSTAFAEV Abstract.

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Various definitions of surface area and volume are possible in finite dimensional normed linear spaces (= Minkowski spaces). Using a Bonnesen-style inequality, we investigate The venerable isoperimetric inequality, for example, is an easy consequence (see [4]). Wirtinger's inequality can be used to derive the more general (planar) Brunn-Minkowski inequality (see [1], p. 115).