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On certain optimal diffeomorphisms between closed curves

Authors
  • Cerri, Andrea
  • Di Fabio, Barbara
Type
Published Article
Journal
Forum Mathematicum
Publisher
De Gruyter
Publication Date
Dec 10, 2011
Volume
26
Issue
6
Pages
1611–1628
Identifiers
DOI: 10.1515/form.2011.172
Source
De Gruyter
Keywords
License
Yellow

Abstract

The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between shape properties of topological spaces, modeled as continuous real-valued functions defined on the spaces themselves. Roughly speaking, the natural pseudo-distance is defined as the infimum of the change of the functions' values, when moving from one space to the other through homeomorphisms, if possible. In this paper, we prove the first available result about the existence of optimal homeomorphisms between closed curves, i.e. inducing a change of the function that equals the natural pseudo-distance. Moreover, we show that, under our assumptions, this optimal homeomorphism is actually a diffeomorphism.

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