Description

• Title:
  Topology of the Grünbaum-Hadwiger-Ramos problem for mass assignments
• Creator:
  Blagojević, Pavle V. M.;
  Loperena, Jaime Calles;
  Crabb, Michael C.;
  Dimitrijević Blagojević, Aleksandra S.
• Description:
  In this paper, motivated by recent work of Schnider and Axelrod-Freed and Soberón, we study an extension of the classical Grünbaum-Hadwiger-Ramos mass partition problem to mass assignments. Using the Fadell-Husseini index theory we prove that for a given family of $j$ mass assignments $\mu_1,\dots,\mu_j$ on the Grassmann manifold $G_{\ell}\big(\mathbb{R}^d\big)$ and a given integer $k\geq 1$ there exist a linear subspace $L\in G_{\ell}\big(\mathbb{R}^d\big)$ and $k$ affine hyperplanes in $L$ that equipart the masses $\mu_1^L,\dots,\mu_j^L$ assigned to the subspace $L$, provided that $d\geq j + (2^{k-1}-1)2^{\lfloor\log_2j\rfloor}$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2023 Pavle V. M. Blagojević, Jaime Calles Loperena, Michael C. Crabb, Aleksandra S. Dimitrijević Blagojević;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2023.03.04
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 61, No 1 (March 2023); 107 - 133;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/42925/35043 ;https://apcz.umk.pl/TMNA/article/view/42925/35044
• Subject:
  Fadell-Husseini ideal valued index;
  mass partitions;
  existence of equivariant maps;
  52A35, 55N25
• Identifier: https://apcz.umk.pl/TMNA/article/view/42925
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other