Extensions of theorems of Rattray and Makeev
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Rattray's theorem, measure partition, Borsuk-Ulam type theoremsAbstrakt
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 $\mathbb{R}^n$ instead of orthonormal bases (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.Pobrania
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2012-04-23
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BLAGOJEVIĆ, Pavle V. M. & KARASEV, Roman. Extensions of theorems of Rattray and Makeev. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2012, T. 40, nr 1, s. 189–213. [udostępniono 22.7.2024].
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