- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Polytopes of Maximal Volume Product
Open Collections
BIRS Workshop Lecture Videos
Featured Collection
BIRS Workshop Lecture Videos
Polytopes of Maximal Volume Product Zvavitch, Artem Mar 26, 2018
mp4
Page Metadata
Item Metadata
Title | Polytopes of Maximal Volume Product |
Creator |
Zvavitch, Artem |
Publisher | Banff International Research Station for Mathematical Innovation and Discovery |
Date Issued | 2018-03-26T15:51 |
Description | For a convex body $K \subset \R^n$, let $$K^z = \{y\in \R^n : \langle y-z, x-z\rangle\le 1, \mbox{\ for all\ } x\in K\}$$ be the polar body of $K$ with respect to the center of polarity $z \in \R^n$. In this talk we would like to discuss the maximum 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 number of vertices bounded by some fixed integer $m \ge n+1$. In particular, we will show that the supremum is reached at a simplicial polytope with exactly $m$ vertices and we provide a new proof of a result of Meyer and Reisner showing that, in the plane, the regular polygon has maximal volume product among all polygons with at most $m$ vertices. |
Extent | 27 minutes |
Subject |
Mathematics Functional analysis Convex and discrete geometry |
Geographic Location | Banff (Alta.) |
Type |
Moving Image |
FileFormat | video/mp4 |
Language | eng |
Notes | Author affiliation: Kent State University |
Series | BIRS Workshop Lecture Videos (Banff, Alta) |
Date Available | 2018-09-23 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
DOI | 10.14288/1.0372137 |
URI | http://hdl.handle.net/2429/67232 |
Affiliation |
Non UBC |
Peer Review Status | Unreviewed |
Scholarly Level | Faculty |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
AggregatedSourceRepository | DSpace |
Download
- Media
- 48630-201803261551-Zvavitch_lrv.mp4 [ 101.5MB ]
- Metadata
- JSON: 48630-1.0372137.json
- JSON-LD: 48630-1.0372137-ld.json
- RDF/XML (Pretty): 48630-1.0372137-rdf.xml
- RDF/JSON: 48630-1.0372137-rdf.json
- Turtle: 48630-1.0372137-turtle.txt
- N-Triples: 48630-1.0372137-rdf-ntriples.txt
- Original Record: 48630-1.0372137-source.json
- Citation
- 48630-1.0372137.ris
Cite
Citation Scheme:
Usage Statistics
Share
Embed
Customize your widget with the following options, then copy and paste the code below into the HTML
of your page to embed this item in your website.
<div id="ubcOpenCollectionsWidgetDisplay">
<script id="ubcOpenCollectionsWidget"
src="{[{embed.src}]}"
data-item="{[{embed.item}]}"
data-collection="{[{embed.collection}]}"
data-metadata="{[{embed.showMetadata}]}"
data-width="{[{embed.width}]}"
async >
</script>
</div>

https://iiif.library.ubc.ca/presentation/dsp.48630.1-0372137/manifest