Duality on Convex Sets in Generalized Regions

Alexander Segal, Boaz A. Slomka

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageEnglish
Title of host publicationAsymptotic Geometric Analysis
Subtitle of host publicationProceedings of the Fall 2010 Fields Institute Thematic Program
EditorsMonika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann
Number of pages10
StatePublished - 2013
Externally publishedYes

Publication series

NameFields Institute Communications
ISSN (Print)1069-5265

Bibliographical note

Funding 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


Dive into the research topics of 'Duality on Convex Sets in Generalized Regions'. Together they form a unique fingerprint.

Cite this