Calculus of Variations and Geometric Measure Theory
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L. Capogna - E. Le Donne - A. Ottazzi

Conformality and $Q$-harmonicity in sub-Riemannian manifolds

created by ledonne on 12 May 2016


Submitted Paper

Inserted: 12 may 2016
Last Updated: 12 may 2016

Pages: 64
Year: 2016

more detailed version of a submitted paper


We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic p-Laplacian operators. For such manifolds we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth. In particular, we prove that contact manifolds support the suitable regularity. The main new technical tools are a sub-Riemannian version of p-harmonic coordinates and a technique of propagation of regularity from horizontal layers.

Keywords: sub-Riemannian geometry, conformal transformation, quasi-conformal maps, subelliptic PDE, harmonic coordinates, Liouville Theorem, Popp measure, morphism property, regularity for p-harmonic functions


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