A Note on Makeev’s Conjectures

R. N. Karasev

doi:10.1007/s10958-016-2679-3

A Note on Makeev’s Conjectures

Authors: Karasev R.N.¹^,2
Affiliations:
1. Moscow Institute of Physics and Technology, Institute for Information Transmission Problems RAS, Moscow
2. Yaroslavl’ State University
Issue: Vol 212, No 5 (2016)
Pages: 521-526
Section: Article
URL: https://journals.rcsi.science/1072-3374/article/view/237045
DOI: https://doi.org/10.1007/s10958-016-2679-3
ID: 237045

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Abstract

A counterexample is given for the Knaster-like Makeev’s conjecture for functions on S². Some particular cases of another conjecture of Makeev on inscribing a quadrangle into a smooth simple closed curve are solved positively.

Keywords

Small Neighborhood, Angular Measure, Unbounded Component, Positive Determinant, Convex Curf

About the authors

R. N. Karasev

Moscow Institute of Physics and Technology, Institute for Information Transmission Problems RAS, Moscow; Yaroslavl’ State University

Author for correspondence.
Email: r_n_karasev@mail.ru
Russian Federation, Yaroslavl’

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