In the second section, differential and algebraic topology are needed to study an amazing generalization of bodies of constant width known as transnormal manifolds. Section 16.3 is devoted to polyhedra that circumscribe the sphere of diameter 1; within this family, we will characterize those ...
On convex bodies of constant width We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in R n is a contractible Hilbert cube man... LE Bazylevych,MM Zarichnyi - 《Topology & Its Applications》 被引量: 79发表: 2004年 On the ...
Oudet, Analytic parametrization of three-dimensional bodies of constant width. Arch. Ration. Mech. Anal. 186/2 , 225–249 (2007)T. Bayen,T. Lachand-Robert,É. Oudet.Analytic Parametrization of Three-Dimensional Bodies of Constant Width[J]. Archive for Rational Mechanics and Analysis .2007...
We define bodies of constant width in $\mathbb{H}^d$ in the standard way as bodies whose all widths are equal. We show that every body of constant width is strictly convex. The minimum width of $C$ over all supporting $H$ is called the thickness $\Delta (C)$ of $C$. A convex...
Nakajima's problem: convex bodies of constant width and constant brightness For a convex body $K\\subset\\R^n$, the $k$th projection function of $K$ assigns to any $k$-dimensional linear subspace of $\\R^n$ the $k$-volume of the orthogonal projection of $K$ to that subspace. ...
This chapter discusses special convex bodies like simplices, ellipsoids, centrally symmetric bodies, and bodies of constant width. A simplex in E d is def... E Heil,H Martini - 《Handbook of Convex Geometry》 被引量: 116发表: 1993年 Inequalities between projection functions of convex bodies....
This chapter discusses special convex bodies like simplices, ellipsoids, centrally symmetric bodies, and bodies of constant width. A simplex in E d is def... E Heil,H Martini - 《Handbook of Convex Geometry》 被引量: 116发表: 1993年 Balancing vectors and Gaussian measures of n -dimensional...
Convex bodies of constant width and constant brightness The kth projection function of a convex body K n assigns to any k-dimensional linear subspace of n the k-volume of the orthogonal projection of K to that s... H Ralph,H Daniel - 《Mathematika》 被引量: 53发表: 2007年 TheLp-curvat...
Convex Bodies of Constant Width A spherical ball obviously has the property that it can be arbitrarily rotated between two fixed parallel planes without losing contact with either plane. It has been known for a long time, certainly since the time of Euler, that there a... GD Chakerian,H ...
On convex bodies of constant width We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in R n is a contractible Hilbert cube man... LE Bazylevych,MM Zarichnyi - 《Topology & Its Applications》 被引量: 79发表: 2004年 Asymmetry ...