p-harmonic coordinates for Hölder metrics and applications
Julin, V., Liimatainen, T., & Salo, M. (2017). p-harmonic coordinates for Hölder metrics and applications. Communications in Analysis and Geometry, 25 (2), 395-430. doi:10.4310/CAG.2017.v25.n2.a5
Julkaistu sarjassa
Communications in Analysis and GeometryPäivämäärä
2017Oppiaine
MatematiikkaTekijänoikeudet
© 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.
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.