Affine invariant points and new constructions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Iurchenko, Ivan¹ 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

关键词: Affine invariant points;    Symmetry;    Convex geometry;   

DOI  :  10.1016/j.jmaa.2016.08.011

来源: Elsevier

【 摘 要 】

In [2] Grunbaum asked if the set of all affine invariant points of a given convex body is equal to the set of all points invariant under every affine automorphism of the body. In [3] we have proven the case of a body with no nontrivial affine automorphisms. After some partial results [6,7] the problem was solved in positive by Mordhorst [8]. In this note we provide an alternative proof of the affirmative answer, developing the ideas of [3]. Moreover, our approach allows us to construct a new large class of affine invariant points. (C) 2016 Published by Elsevier Inc.

【 授权许可】

Free