FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 2, PAGES 153-156

An open family of sets that have several minimal fillings

Z. N. Ovsyannikov

Abstract

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Minimal fillings of $n$-point metric spaces were introduced by Ivanov and Tuzhilin. It was thought that "for almost all sets" in some sense such a filling is unique. Here we introduce a counterexample to this hypothesis.

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Last modified: January 7, 2014