Affine hemispheres of elliptic type

B. Klartag

doi:https://doi.org/10.1090/spmj/1484

Affine hemispheres of elliptic type

B. Klartag

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We find that for any n-dimensional, compact, convex set K ⊆ R ⁿ⁺¹ there is an affinely-spherical hypersurface M ⊆ R ⁿ⁺¹ with center in the relative interior of K such that the disjoint union M ∪ K is the boundary of an (n + 1)- dimensional, compact, convex set. This so-called affine hemisphere M is uniquely determined by K up to affine transformations, it is of elliptic type, is associated with K in an affinely-invariant manner, and it is centered at the Santaló point of K.

Original language	English
Pages (from-to)	107-138
Number of pages	32
Journal	St. Petersburg Mathematical Journal
Volume	29
Issue number	1
Early online date	27 Dec 2017
DOIs	https://doi.org/10.1090/spmj/1484
State	Published - 1 Jan 2018

Keywords

Affine sphere
Anchor
Cone measure
Obverse
Santaló point

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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http://arxiv.org/abs/1508.00474License: Other

Cite this

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AB - We find that for any n-dimensional, compact, convex set K ⊆ R n+1 there is an affinely-spherical hypersurface M ⊆ R n+1 with center in the relative interior of K such that the disjoint union M ∪ K is the boundary of an (n + 1)- dimensional, compact, convex set. This so-called affine hemisphere M is uniquely determined by K up to affine transformations, it is of elliptic type, is associated with K in an affinely-invariant manner, and it is centered at the Santaló point of K.

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KW - Cone measure

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Affine hemispheres of elliptic type

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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