Extensions of theorems of Rattray and Makeev
Keywords
Rattray's theorem, measure partition, Borsuk-Ulam type theoremsAbstract
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.Downloads
Published
2012-04-23
How to Cite
1.
BLAGOJEVIĆ, Pavle V. M. and KARASEV, Roman. Extensions of theorems of Rattray and Makeev. Topological Methods in Nonlinear Analysis. Online. 23 April 2012. Vol. 40, no. 1, pp. 189 - 213. [Accessed 13 December 2024].
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