Convex Bodies of Minimal Volume, Surface Area and Mean Width with Respect to Thin Shells
نویسندگان
چکیده
Given r > 1, we consider the minimal volume, minimal surface area and minimal mean width of convex bodies in E that contain a unit ball, and the extreme points are of distance at least r from the centre of the unit ball; more precisely, we investigate the difference of these minimums and of the volume, surface area and mean width, respectively, of the unit ball. As r tends to one, we describe the asymptotic behaviour of the differences, and describe the typical faces of the extremal bodies in E3. AMS classification: 52A27, 52A40 Supported by OTKA grants T 043556 and 033752 Supported by OTKA grants T 042769, 043520 and 049301 Supported by the Marie Curie Research Training Network PhD
منابع مشابه
Numerical simulation of Laminar Free Convection Heat Transfer around Isothermal Concave and Convex Body Shapes
In the present research, free convection heat transfer from isothermal concave and convex body shapes is studied numerically. The body shapes investigated here, are bi-sphere, cylinder, prolate and cylinder with hemispherical ends; besides, they have the same height over width (H/D = 2). A Numerical simulation is implemented to obtain heat transfer and fluid flow from all of the geometries in a...
متن کاملTypical faces of extremal polytopes with respect to a thin three-dimensional shell
Given r > 1, we search for the convex body of minimal volume in E3 that contains a unit ball, and whose extreme points are of distance at least r from the centre of the unit ball. It is known that the extremal body is the regular octahedron and icosahedron for suitable values of r. In this paper we prove that if r is close to one then the typical faces of the extremal body are asymptotically re...
متن کاملComparison of Two Kinds of Functionally Graded Cylindrical Shells with Various Volume Fraction Laws for Vibration Analysis
In this paper, a study on the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The effects of the FGM configuration are taken into account by studying the frequencies of two FG cylindrical shells. Type I FG cylindrical shell has nickel on its inner surface and stainless steel on its outer surface and Type II...
متن کاملAnalytic parametrization and volume minimization of three dimensional bodies of constant width
We present a complete analytic parametrization of constant width bodies in dimension 3 based on the median surface: more precisely, we define a bijection between some space of functions and constant width bodies. We compute simple geometrical quantities like the volume and the surface area in terms of those functions. As a corollary we give a new algebraic proof of Blaschke’s formula. Finally, ...
متن کاملApproximation of Smooth Convex Bodies by Random Circumscribed Polytopes
Choose n independent random points on the boundary of a convex body K ⊂Rd . The intersection of the supporting halfspaces at these random points is a random convex polyhedron. The expectations of its volume, its surface area and its mean width are investigated. In the case that the boundary of K is sufficiently smooth, asymptotic expansions as n→∞ are derived even in the case when the curvature...
متن کامل