Triangulation of diffeomorphisms

Tadeusz Iwaniec; Jani Onninen

doi:10.1007/s00208-016-1426-x

Triangulation of diffeomorphisms

Tadeusz Iwaniec, Jani Onninen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1133-1169
Number of pages	37
Journal	Mathematische Annalen
Volume	368
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-016-1426-x
State	Published - Aug 1 2017

Keywords

Primary 41A45
Secondary 57R05

ASJC Scopus subject areas

Mathematics(all)

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Triangulation of diffeomorphisms

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Keywords

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