Authors: Blagojević, Pavle 
Dimitrijević-Blagojević, Aleksandra 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A problem related to Bárány-Grünbaum conjecture
Journal: Filomat
Volume: 27
Issue: 1
First page: 109
Last page: 113
Issue Date: 19-Jul-2013
Rank: M21
ISSN: 0354-5180
DOI: 10.2298/FIL1301109B
Abstract: 
In this paper we prove that for any absolute continuous Borel probability measure μ on the sphere S2 and any t ∈ [0; 1/4 ] there exist four great semi-circles l1,..., l4 emanating from a point x 2 S2 that partition sphere S2 into four angular sectors σ1,..., σ4, counter clockwise oriented, such that μ(σ1) = μ(σ4) = t; μ(σ2) = μ(σ3) = 1/4 - t, and area(σ1) = area(σ4); area(σ2) = area(σ3).
Keywords: Existence of equivariant maps | Measure partitions | Serre spectral sequence
Publisher: Faculty of Sciences and Mathematics, University of Niš
Project: European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC, Grant agreement no. 247029-SDModels
Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 

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