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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