Description

• Title:
  Extensions of theorems of Rattray and Makeev
• Creator:
  Blagojević, Pavle V. M.;
  Karasev, Roman
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2012.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 40, No 1 (September 2012); 189 - 213;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.028/8377
• Subject:
  Rattray's theorem;
  measure partition;
  Borsuk-Ulam type theorems;
  55M20;
  05D10;
  20J06;
  46B20;
  52A21;
  55M35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.028
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other