Triangulation of diffeomorphisms

Research output: Contribution to journalArticle

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)1-37
Number of pages37
JournalMathematische Annalen
DOIs
StateAccepted/In press - May 23 2016

ASJC Scopus subject areas

  • Mathematics(all)

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