.png){kind=icon}
.png){kind=icon}
Return
Variants of a theorem of Macbeath in finite-dimensional normed spaces
.png){kind=icon}
OA
AI
DOI：10.1112/mtk.70078.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
A classical theorem of Macbeath states that for any integers , , -dimensional Euclidean balls are hardest to approximate, in terms of volume difference, by inscribed convex polytopes with vertices. In this paper, we investigate normed variants of this problem: we intend to find the extremal values of the Busemann volume, Holmes-Thompson volume, Gromov's mass, and Gromov's of a largest volume convex polytope with vertices, inscribed in the unit ball of a -dimensional normed space.
Keywords:
Macbeath theorem
normed spaces
convex polytopes
Busemann volume
Holmes-Thompson volume
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.