Triangulation of diffeomorphisms

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2 Scopus citations

Abstract

Is it possible to approximate a diffeomorphism of Euclidean domains with piecewise affine homeomorphisms, locally uniformly up to the first order derivatives? The answer is yes. However, any effort to provide a rigorous and clear proof reveals the complexity of this question, especially in higher dimensions. It is the objective of the present paper to formulate this question in its greatest generality, as well as to provide all details for the affirmative answer, Theorem 1.1. A novelty, which has broader applications, is the construction of selfsimilar isotropic triangulation of the Euclidean domains, Theorem 1.2.

Original languageEnglish (US)
Pages (from-to)1133-1169
Number of pages37
JournalMathematische Annalen
Volume368
Issue number3-4
DOIs
StatePublished - Aug 1 2017

Keywords

  • Primary 41A45
  • Secondary 57R05

ASJC Scopus subject areas

  • Mathematics(all)

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