Conformality and Q-harmonicity in Sub-Riemannian Manifolds

Authors

Luca Capogna, Worcester Polytechnic InstituteFollow
Giovanna Citti, Alma Mater Studiorum Università di Bologna
Enrico Le Donne, University of Jyväskylä
Alessandro Ottazzi, UNSW Sydney

Document Type

Article

Publication Date

2-1-2019

Publication Title

Journal des Mathematiques Pures et Appliquees

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

Harmonic coordinates, Liouville Theorem, Quasi-conformal maps, Regularity for p-harmonic functions, Sub-Riemannian geometry, Subelliptic PDE

Volume

122

First Page

67

Last Page

124

DOI

10.1016/j.matpur.2017.12.006

ISSN

00217824

Comments

Author’s submitted manuscript.

Recommended Citation

Capogna, Luca; Citti, Giovanna; Le Donne, Enrico; and Ottazzi, Alessandro, "Conformality and Q-harmonicity in Sub-Riemannian Manifolds" (2019). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/126