Recently, the duality relation on several families of convex sets was shown to be completely characterized by the simple property of reversing order. The families discussed in aforementioned results were convex sets in ℝn. Our goal in this note is to generalize this type of results to regions in ℝn bounded between two convex sets.
|Title of host publication||Asymptotic Geometric Analysis|
|Subtitle of host publication||Proceedings of the Fall 2010 Fields Institute Thematic Program|
|Editors||Monika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann|
|Number of pages||10|
|State||Published - 2013|
|Name||Fields Institute Communications|
Bibliographical noteFunding Information:
The authors would like to thank Prof. Vitali Milman and Prof. Shiri Artstein for suggesting to consider this generalization of order isomorphisms for convex regions and their useful advice and comments. The first named author was partially supported by the ISF grant no. 387/09, and the second named author was partially supported by the ISF grant no. 247/11. The research is supported in part by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.
- Duality of convex bodies
- Fractional linear transformations
- Order isomorphism