Optimal homeomorphisms between closed curves

Details Optimal homeomorphisms between closed curves Optimal homeomorphisms between closed curves

2009-06-25

arxiv.org/abs/0906.4648v1

Mathematics

Differential Geometry

11 pages, 3 figures

Scientific paper

The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. 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.

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