Authors: Blagojević, Pavle 
Karasev, Roman
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Extensions of theorems of Rattray and Makeev
Journal: Topological Methods in Nonlinear Analysis
Volume: 40
Issue: 1
First page: 189
Last page: 213
Issue Date: 1-Dec-2012
Rank: M21
ISSN: 1230-3429
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 ℝn 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.
Keywords: Borsuk-ulam type theorems | Measure partition | Rattray's theorem
Publisher: Juliusz Schauder University Centre for Nonlinear Studies

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