Duality on Convex Sets in Generalized Regions

Alexander Segal; Boaz A. Slomka

doi:10.1007/978-1-4614-6406-8_13

Duality on Convex Sets in Generalized Regions

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

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 language	English
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
Pages	289-298
Number of pages	10
DOIs	https://doi.org/10.1007/978-1-4614-6406-8_13
State	Published - 2013
Externally published	Yes

Publication series

Name	Fields Institute Communications
Volume	68
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.

Keywords

Duality of convex bodies
Fractional linear transformations
Order isomorphism

Access to Document

10.1007/978-1-4614-6406-8_13

Cite this

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Duality on Convex Sets in Generalized Regions. / Segal, Alexander; Slomka, Boaz A.
Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program. ed. / Monika Ludwig; Vladimir Pestov; Vitali Milman; Nicole Tomczak-Jaegermann. 2013. p. 289-298 (Fields Institute Communications; Vol. 68).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Duality on Convex Sets in Generalized Regions

Abstract

Publication series

Bibliographical note

Keywords

Access to Document

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