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arXiv · 1011.0869

Extensions of theorems of Rattray and Makeev

Pavle Blagojević·Roman Karasev
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Abstract

We consider extensions of the Rattray theorem and two Makeev's theorems, showing that they hold for several maps, measures, or functions simultaneously, when we consider orthonormal $k$-frames in $\R^n$ instead of orthonormal basis (full frames). We also present new results on simultaneous partition of several measures into parts by $k$ mutually orthogonal hyperplanes. In the case $k=2$ we relate the Rattray and Makeev type results with the well known embedding problem for projective spaces.

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Pavle Blagojević, Roman Karasev. 2012-04-13. Extensions of theorems of Rattray and Makeev. https://arxiv.org/abs/1011.0869

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