A1 Journal article (refereed)
Conformality and Q-harmonicity in sub-Riemannian manifolds (2019)
Capogna, L., Citti, G., Le Donne, E., & Ottazzi, A. (2019). Conformality and Q-harmonicity in sub-Riemannian manifolds. Journal de Mathematiques Pures et Appliquees, 122, 67-124. https://doi.org/10.1016/j.matpur.2017.12.006
JYU authors or editors
Publication details
All authors or editors: Capogna, Luca; Citti, Giovanna; Le Donne, Enrico; Ottazzi, Alessandro
Journal or series: Journal de Mathematiques Pures et Appliquees
ISSN: 0021-7824
eISSN: 1776-3371
Publication year: 2019
Volume: 122
Issue number: 0
Pages range: 67-124
Publisher: Elsevier Masson
Publication country: France
Publication language: English
DOI: https://doi.org/10.1016/j.matpur.2017.12.006
Publication open access: Not open
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/62534
Abstract
We establish regularity of conformal maps between sub-Riemannian manifolds from regularity of Q-harmonic functions, and in particular we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth in all contact sub-Riemannian manifolds. Together with the recent results in [15], our work yields a new proof of the smoothness of boundary extensions of biholomorphims between strictly pseudoconvex smooth domains [29].
Keywords: differential geometry; partial differential equations; manifolds (mathematics)
Free keywords: conformal transformation; quasi-conformal maps; subelliptic PDE; harmonic coordinates; Liouville theorem; popp measure; morphism property; regularity for p-harmonic functions; sub-Riemannian geometry
Contributing organizations
Related projects
- MAnET Metric Analysis for Emergent Technologies
- Koskela, Pekka
- European Commission
- Geometry of subRiemannian groups: regularity of finite-perimeter sets, geodesics, spheres, and isometries with applications and generalizations to biLipschitz homogenous spaces
- Le Donne, Enrico
- Research Council of Finland
Ministry reporting: Yes
Reporting Year: 2019
JUFO rating: 3