Affine invariant points and new constructions

Ivan Iurchenko

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arXiv · 1608.06657

Affine invariant points and new constructions

Ivan Iurchenko

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Abstract

In \cite{branko} Gr{\"u}nbaum 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 \cite{ivan} we have proven the case of a body with no nontrivial affine automorphisms. After some partial results (\cite{aip},\cite{newaip}) the problem was solved in positive by Mordhorst \cite{Olaf}. In this note we provide an alternative proof of the affirmative answer, developing the ideas of \cite{ivan}. Moreover, our approach allows us to construct a new large class of affine invariant points.

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Ivan Iurchenko. 2016-08-23. Affine invariant points and new constructions. https://arxiv.org/abs/1608.06657

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