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arXiv · 1505.00459

A contribution to the Aleksandrov conservative distance problem in two dimensions

György Pál Gehér
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Abstract

Let $E$ be a two-dimensional real normed space. In this paper we show that if the unit circle of $E$ does not contain any line segment such that the distance between its endpoints is greater than 1, then every transformation $\phi\colon E\to E$ which preserves the unit distance is automatically an affine isometry. In particular, this condition is satisfied when the norm is strictly convex.

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György Pál Gehér. 2015-05-03. A contribution to the Aleksandrov conservative distance problem in two dimensions. https://doi.org/10.1016/j.laa.2015.05.005

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