Triangulation of diffeomorphisms

Tadeusz Iwaniec; Jani Kristian Onninen

doi:10.1007/s00208-016-1426-x

Triangulation of diffeomorphisms

Tadeusz Iwaniec, Jani Kristian Onninen

Department of Mathematics

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

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)	1-37
Number of pages	37
Journal	Mathematische Annalen
DOIs	https://doi.org/10.1007/s00208-016-1426-x
State	Accepted/In press - May 23 2016

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s00208-016-1426-x

Fingerprint Dive into the research topics of 'Triangulation of diffeomorphisms'. Together they form a unique fingerprint.

Cite this

@article{4547e67e49da496a9aa35e3eac84b837,

title = "Triangulation of diffeomorphisms",

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.",

author = "Tadeusz Iwaniec and Onninen, {Jani Kristian}",

year = "2016",

month = may,

day = "23",

doi = "10.1007/s00208-016-1426-x",

language = "English (US)",

pages = "1--37",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

}

TY - JOUR

T1 - Triangulation of diffeomorphisms

AU - Iwaniec, Tadeusz

AU - Onninen, Jani Kristian

PY - 2016/5/23

Y1 - 2016/5/23

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84969808334&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969808334&partnerID=8YFLogxK

U2 - 10.1007/s00208-016-1426-x

DO - 10.1007/s00208-016-1426-x

M3 - Article

AN - SCOPUS:84969808334

SP - 1

EP - 37

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

ER -