p-harmonic coordinates for Hölder metrics and applications
Abstract
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.
Main Authors
Format
Articles
Research article
Published
2017
Series
Subjects
Publication in research information system
Publisher
International Press
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201801121163Use this for linking
Review status
Peer reviewed
ISSN
1019-8385
DOI
https://doi.org/10.4310/CAG.2017.v25.n2.a5
Language
English
Published in
Communications in Analysis and Geometry
Citation
- 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
License
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.