Authors: Bárány, Imre
Blagojević, Pavle 
Dimitrijević-Blagojević, Aleksandra 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Functions, Measures, and Equipartitioning Convex k-Fans
Journal: Discrete and Computational Geometry
Volume: 49
Issue: 2
First page: 382
Last page: 401
Issue Date: 1-Jan-2013
Rank: M22
ISSN: 0179-5376
DOI: 10.1007/s00454-012-9467-8
A k-fan in the plane is a point x∈ℝ2 and k halflines starting from x. There are k angular sectors σ1,...,σk between consecutive halflines. The k-fan is convex if every sector is convex. A (nice) probability measure μ is equipartitioned by the k-fan if μ(σi)=1/k for every sector. One of our results: Given a nice probability measure μ and a continuous function f defined on sectors, there is a convex 5-fan equipartitioning μ with f(σ1)=f(σ2)=f(σ3).
Keywords: Convex k-fans | Equipartitions | Functions on sectors | Measures
Publisher: Springer Link
Project: European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC, Grant agreement no. 247029-SDModels
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