Conformality and Q-harmonicity in sub-Riemannian manifolds
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
Published inJournal de Mathematiques Pures et Appliquees
© 2017 Elsevier Masson SAS
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 , our work yields a new proof of the smoothness of boundary extensions of biholomorphims between strictly pseudoconvex smooth domains .
Publication in research information system
MetadataShow full item record
Related funder(s)European Commission; Academy of Finland
Funding program(s)FP7 (EU's 7th Framework Programme); Academy Research Fellow, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingPartially funded by NSF awards DMS 1449143 and DMS 1503683.2. Partially funded by the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007–2013/ under REA grant agreement No. 607643 and by the European Unions Horizon 2020 research programme, Marie Skłodowska-Curie grant agreement No. 777822. 3. Supported by the Academy of Finland, project No. 288501.4. Partially supported by the Australian Research Council, project No. DP140100531. ...
Showing items with similar title or keywords.
Le Donne, Enrico; Lučić, Danka; Pasqualetto, Enrico (Springer, 2022)We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations ...
A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries Le Donne, Enrico (De Gruyter Open, 2017)Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with ...
Nicolussi Golo, Sebastiano (University of Jyväskylä, 2017)
Angulo, Pablo; Faraco, Daniel; Guijarro, Luis; Salo, Mikko (American Mathematical Society, 2020)We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, $ 3$-manifolds, and $ 4$-manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman ...
Parkkonen, Jouni; Paulin, Frédéric (Universite Clermont Auvergne, 2022)In this paper, we prove an analog of Cartan’s theorem, saying that the chain-preserving transformations of the boundary of the quaternionic hyperbolic spaces are projective transformations. We give a counting and ...