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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 27, Issue 3


The natural pseudo-distance as a quotient pseudo-metric, and applications

Francesca Cagliari / Barbara Di Fabio / Claudia Landi
Published Online: 2013-05-28 | DOI: https://doi.org/10.1515/forum-2012-0152


The natural pseudo-distance is a similarity measure conceived for the purpose of comparing shapes. In this paper we revisit this pseudo-metric from the point of view of quotients. In particular, we show that the natural pseudo-distance coincides with the quotient pseudo-metric on the space of continuous functions on a compact manifold, endowed with the uniform convergence metric, modulo self-homeomorphisms of the manifold. As applications of this result, the natural pseudo-distance is shown to be actually a metric on a number of function subspaces such as the space of topological embeddings, of isometries, and of simple Morse functions on surfaces.

Keywords: Function space; Morse function; homeomorphism group action; isometry; shape comparison

MSC: 54C35; 57S25; 18A32; 68U05; 54E35

About the article

Received: 2012-10-08

Revised: 2013-03-18

Published Online: 2013-05-28

Published in Print: 2015-05-01

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1729–1742, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0152.

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