- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Polytopes of Maximal Volume Product
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Polytopes of Maximal Volume Product Alexander, Matt
Description
We will discuss the maximal values of the volume product $\mathcal{P}(K)=\min_{z\in {\rm int}(K)}|K|||K^z|$, among convex polytopes $K\subset {\mathbb R}^n$ with a bounded number of vertices where $K^z = \{y\in{\mathbb R}^n : (y-z) \cdot(x-z)\le 1, \mbox{\ for all\ } x\in K\}$ is the polar body of $K$ with respect to the center of polarity $z$. In particular, we will discuss polytopes with $n+2$ vertices in $\RR^n$, symmetric polytopes with $8$ vertices in $\mathbb{R}^3$, and that the supremum is reached at a simplicial polytope with exactly $m$ vertices for all convex bodies of $m$ or fewer vertices.
Item Metadata
Title |
Polytopes of Maximal Volume Product
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2017-05-25T16:19
|
Description |
We will discuss the maximal values of the volume product $\mathcal{P}(K)=\min_{z\in {\rm int}(K)}|K|||K^z|$, among convex polytopes $K\subset {\mathbb R}^n$ with a bounded number of vertices where $K^z = \{y\in{\mathbb R}^n : (y-z) \cdot(x-z)\le 1, \mbox{\ for all\ } x\in K\}$ is the polar body of $K$ with respect to the center of polarity $z$. In particular, we will discuss polytopes with $n+2$ vertices in $\RR^n$, symmetric polytopes with $8$ vertices in $\mathbb{R}^3$, and that the supremum is reached at a simplicial polytope with exactly $m$ vertices for all convex bodies of $m$ or fewer vertices.
|
Extent |
33 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Kent State University
|
Series | |
Date Available |
2017-11-23
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0360664
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Graduate
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International