pharmoniccagfinaldraft.pdf
Final Draft

p-harmonic coordinates for Hölder metrics and applications

Abstrakti
We show that on any Riemannian manifold with H¨older continuous metric tensor, there exists a p-harmonic coordinate system near any point. When p = n this leads to a useful gauge condition for regularity results in conformal geometry. As applications, we show that any conformal mapping between manifolds having C α metric tensors is C 1+α regular, and that a manifold with W1,n ∩ C α metric tensor and with vanishing Weyl tensor is locally conformally flat if n ≥ 4. The results extend the works [LS14, LS15] from the case of C 1+α metrics to the H¨older continuous case. In an appendix, we also develop some regularity results for overdetermined elliptic systems in divergence form.
Päätekijät
Julin, Vesa Liimatainen, Tony Salo, Mikko
Aineistotyyppi
Artikkelit Tutkimusartikkeli
Julkaistu
2017
Sarja
Communications in Analysis and Geometry
Aiheet
p-harmonic coordinates
Hölder metrics
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/27147515
Julkaisija
International Press
Julkaisun pysyvä osoite
https://urn.fi/URN:NBN:fi:jyu-201801121163Käytä tätä linkitykseen
Vertaisarvioinnin tila
Vertaisarvioitu
ISSN
1019-8385
DOI
https://doi.org/10.4310/CAG.2017.v25.n2.a5
Kieli
englanti
Julkaisussa
Communications in Analysis and Geometry
Viite
Lisenssi
Open Access
Copyright© the Authors, 2017. This is a final draft version of an article whose final and definitive form has been published by International Press. Published in this repository with the kind permission of the publisher.

Jaa

_version_ 1824577754951057408
accesslevel_txtF openAccess
author Julin, Vesa Liimatainen, Tony Salo, Mikko
author_facet Julin, Vesa Liimatainen, Tony Salo, Mikko
departments_txtF_mv Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics
description We show that on any Riemannian manifold with H¨older continuous metric tensor, there exists a p-harmonic coordinate system near any point. When p = n this leads to a useful gauge condition for regularity results in conformal geometry. As applications, we show that any conformal mapping between manifolds having C α metric tensors is C 1+α regular, and that a manifold with W1,n ∩ C α metric tensor and with vanishing Weyl tensor is locally conformally flat if n ≥ 4. The results extend the works [LS14, LS15] from the case of C 1+α metrics to the H¨older continuous case. In an appendix, we also develop some regularity results for overdetermined elliptic systems in divergence form.
digitoitu_txtF no
discipline_txtF Inversio-ongelmien huippuyksikkö
files_txt [{"restricted": "no", "bundleName": "THUMBNAIL", "format": "JPEG", "mimeType": "image/jpeg", "name": "pharmoniccagfinaldraft.pdf.jpg", "description": "Generated Thumbnail", "retrieveLink": "/rest/bitstreams/7a8a8e90-a309-4df2-b0b3-13506457193c/retrieve"}, {"restricted": "no", "bundleName": "ORIGINAL", "format": "Adobe PDF", "mimeType": "application/pdf", "name": "pharmoniccagfinaldraft.pdf", "description": "Final Draft", "retrieveLink": "/rest/bitstreams/d49113b0-d2f1-4da9-9058-934c46c6dc8c/retrieve"}, {"restricted": "no", "bundleName": "LICENSE", "format": "License", "mimeType": "text/plain", "name": "license.txt", "description": null, "retrieveLink": "/rest/bitstreams/f5c4e483-ea5e-4ab4-bc93-af1d42deea99/retrieve"}, {"restricted": "no", "bundleName": "LICENSE", "format": "Adobe PDF", "mimeType": "application/pdf", "name": "Communications in Analysis and Geometry_LUPA.pdf", "description": "", "retrieveLink": "/rest/bitstreams/9efd9ebc-2c7c-4ceb-9b5f-a3b0a803c6d7/retrieve"}, {"restricted": "no", "bundleName": "TEXT", "format": "Text", "mimeType": "text/plain", "name": "pharmoniccagfinaldraft.pdf.txt", "description": "Extracted text", "retrieveLink": "/rest/bitstreams/81805667-d073-4514-8a1c-3f4db470aa35/retrieve"}]
format 0/Artikkelit/ 1/Artikkelit/research article/
fullrecord
key : dc.contributor.author
value : Julin, Vesa
language :
element : contributor
qualifier : author
schema : dc
key : dc.contributor.author
value : Liimatainen, Tony
language :
element : contributor
qualifier : author
schema : dc
key : dc.contributor.author
value : Salo, Mikko
language :
element : contributor
qualifier : author
schema : dc
key : dc.date.accessioned
value : 2018-01-15T10:12:49Z
language :
element : date
qualifier : accessioned
schema : dc
key : dc.date.available
value : 2018-01-15T10:12:49Z
language :
element : date
qualifier : available
schema : dc
key : dc.date.issued
value : 2017
language :
element : date
qualifier : issued
schema : dc
key : dc.identifier.citation
value : Julin, V., Liimatainen, T., & Salo, M. (2017). p-harmonic coordinates for Hölder metrics and applications. Communications in Analysis and Geometry, 25(2), 395-430. https://doi.org/10.4310/CAG.2017.v25.n2.a5
language :
element : identifier
qualifier : citation
schema : dc
key : dc.identifier.other
value : jyu-pub.27147515
language :
element : identifier
qualifier : other
schema : dc
key : dc.identifier.uri
value : https://jyx.jyu.fi/handle/123456789/56719
language :
element : identifier
qualifier : uri
schema : dc
key : dc.description.abstract
value : We show that on any Riemannian manifold with H¨older continuous metric tensor, there exists a p-harmonic coordinate system near any point. When p = n this leads to a useful gauge condition for regularity results in conformal geometry. As applications, we show that any conformal mapping between manifolds having C α metric tensors is C 1+α regular, and that a manifold with W1,n ∩ C α metric tensor and with vanishing Weyl tensor is locally conformally flat if n ≥ 4. The results extend the works [LS14, LS15] from the case of C 1+α metrics to the H¨older continuous case. In an appendix, we also develop some regularity results for overdetermined elliptic systems in divergence form.
language :
element : description
qualifier : abstract
schema : dc
key : dc.language.iso
value : eng
language :
element : language
qualifier : iso
schema : dc
key : dc.publisher
value : International Press
language :
element : publisher
qualifier :
schema : dc
key : dc.relation.ispartofseries
value : Communications in Analysis and Geometry
language :
element : relation
qualifier : ispartofseries
schema : dc
key : dc.subject.other
value : p-harmonic coordinates
language :
element : subject
qualifier : other
schema : dc
key : dc.subject.other
value : Hölder metrics
language :
element : subject
qualifier : other
schema : dc
key : dc.title
value : p-harmonic coordinates for Hölder metrics and applications
language :
element : title
qualifier :
schema : dc
key : dc.type
value : research article
language :
element : type
qualifier :
schema : dc
key : dc.identifier.urn
value : URN:NBN:fi:jyu-201801121163
language :
element : identifier
qualifier : urn
schema : dc
key : dc.contributor.department
value : Matematiikan ja tilastotieteen laitos
language : fi
element : contributor
qualifier : department
schema : dc
key : dc.contributor.department
value : Department of Mathematics and Statistics
language : en
element : contributor
qualifier : department
schema : dc
key : dc.subject.discipline
value : Matematiikka
language : fi
element : subject
qualifier : discipline
schema : dc
key : dc.subject.discipline
value : Analyysin ja dynamiikan tutkimuksen huippuyksikkö
language : fi
element : subject
qualifier : discipline
schema : dc
key : dc.subject.discipline
value : Inversio-ongelmien huippuyksikkö
language : fi
element : subject
qualifier : discipline
schema : dc
key : dc.subject.discipline
value : Mathematics
language : en
element : subject
qualifier : discipline
schema : dc
key : dc.subject.discipline
value : Analysis and Dynamics Research (Centre of Excellence)
language : en
element : subject
qualifier : discipline
schema : dc
key : dc.subject.discipline
value : Centre of Excellence in Inverse Problems
language : en
element : subject
qualifier : discipline
schema : dc
key : dc.type.uri
value : http://purl.org/eprint/type/JournalArticle
language :
element : type
qualifier : uri
schema : dc
key : dc.date.updated
value : 2018-01-12T10:15:11Z
language :
element : date
qualifier : updated
schema : dc
key : dc.type.coar
value : http://purl.org/coar/resource_type/c_2df8fbb1
language :
element : type
qualifier : coar
schema : dc
key : dc.description.reviewstatus
value : peerReviewed
language :
element : description
qualifier : reviewstatus
schema : dc
key : dc.format.pagerange
value : 395-430
language :
element : format
qualifier : pagerange
schema : dc
key : dc.relation.issn
value : 1019-8385
language :
element : relation
qualifier : issn
schema : dc
key : dc.relation.numberinseries
value : 2
language :
element : relation
qualifier : numberinseries
schema : dc
key : dc.relation.volume
value : 25
language :
element : relation
qualifier : volume
schema : dc
key : dc.type.version
value : acceptedVersion
language :
element : type
qualifier : version
schema : dc
key : dc.rights.copyright
value : © the Authors, 2017. This is a final draft version of an article whose final and definitive form has been published by International Press. Published in this repository with the kind permission of the publisher.
language :
element : rights
qualifier : copyright
schema : dc
key : dc.rights.accesslevel
value : openAccess
language : fi
element : rights
qualifier : accesslevel
schema : dc
key : dc.type.publication
value : article
language :
element : type
qualifier : publication
schema : dc
key : dc.relation.doi
value : 10.4310/CAG.2017.v25.n2.a5
language :
element : relation
qualifier : doi
schema : dc
key : dc.type.okm
value : A1
language :
element : type
qualifier : okm
schema : dc
files : [{"restricted":"no","bundleName":"THUMBNAIL","format":"JPEG","mimeType":"image\/jpeg","name":"pharmoniccagfinaldraft.pdf.jpg","description":"Generated Thumbnail","retrieveLink":"\/rest\/bitstreams\/7a8a8e90-a309-4df2-b0b3-13506457193c\/retrieve"},{"restricted":"no","bundleName":"ORIGINAL","format":"Adobe PDF","mimeType":"application\/pdf","name":"pharmoniccagfinaldraft.pdf","description":"Final Draft","retrieveLink":"\/rest\/bitstreams\/d49113b0-d2f1-4da9-9058-934c46c6dc8c\/retrieve"},{"restricted":"no","bundleName":"LICENSE","format":"License","mimeType":"text\/plain","name":"license.txt","description":null,"retrieveLink":"\/rest\/bitstreams\/f5c4e483-ea5e-4ab4-bc93-af1d42deea99\/retrieve"},{"restricted":"no","bundleName":"LICENSE","format":"Adobe PDF","mimeType":"application\/pdf","name":"Communications in Analysis and Geometry_LUPA.pdf","description":"","retrieveLink":"\/rest\/bitstreams\/9efd9ebc-2c7c-4ceb-9b5f-a3b0a803c6d7\/retrieve"},{"restricted":"no","bundleName":"TEXT","format":"Text","mimeType":"text\/plain","name":"pharmoniccagfinaldraft.pdf.txt","description":"Extracted text","retrieveLink":"\/rest\/bitstreams\/81805667-d073-4514-8a1c-3f4db470aa35\/retrieve"}]
id jyx_123456789_56719
ispartofseries_txtF_mv Communications in Analysis and Geometry
issn 1019-8385
language_txtF_mv eng
okm_txtF A1
online_urls_str_mv URN:NBN:fi:jyu-201801121163
publishDate 2017
publisher_txtF_mv International Press
reviewstatus_txtF peerReviewed
series Communications in Analysis and Geometry
spellingShingle p-harmonic coordinates for Hölder metrics and applications Julin, Vesa Liimatainen, Tony Salo, Mikko p-harmonic coordinates Hölder metrics Communications in Analysis and Geometry
thumbnail https://jyx.jyu.fi/bitstreams/7a8a8e90-a309-4df2-b0b3-13506457193c/download.jpg?sequence=99
title p-harmonic coordinates for Hölder metrics and applications
title_full p-harmonic coordinates for Hölder metrics and applications
title_fullStr p-harmonic coordinates for Hölder metrics and applications
title_full_unstemmed p-harmonic coordinates for Hölder metrics and applications
title_short p-harmonic coordinates for Hölder metrics and applications
title_sort pharmonic coordinates for Hölder metrics and applications
topic p-harmonic coordinates Hölder metrics

Samankaltaisia teoksia