Cerri, Andrea ; Di Fabio , Barbara
(2010)
On certain optimal diffeomorphisms between closed curves.
[Preprint]
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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.
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.
Document type
Preprint
Creators
Additional Information
2010 Mathematics Subject Classification. Primary 57S05, 57S10; Secondary 54C30, 68U05.
Keywords
Natural pseudo-distance, measuring function, Morse function, Size Theory.
Subjects
DOI
Deposit date
29 Apr 2011 11:20
Last modified
16 May 2011 12:17
URI
Other metadata
Document type
Preprint
Creators
Additional Information
2010 Mathematics Subject Classification. Primary 57S05, 57S10; Secondary 54C30, 68U05.
Keywords
Natural pseudo-distance, measuring function, Morse function, Size Theory.
Subjects
DOI
Deposit date
29 Apr 2011 11:20
Last modified
16 May 2011 12:17
URI
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