6533b835fe1ef96bd129ea53
RESEARCH PRODUCT
Conformality and $Q$-harmonicity in sub-Riemannian manifolds
Giovanna CittiLuca CapognaEnrico Le DonneAlessandro Ottazzisubject
Harmonic coordinatesMathematics - Differential GeometryPure mathematicsWork (thermodynamics)morphism propertyGeneral Mathematicsconformal transformationBoundary (topology)Conformal map01 natural sciencesdifferentiaaligeometriaMathematics - Analysis of PDEsMathematics - Metric GeometryLiouville TheoremRegularity for p-harmonic functionSubelliptic PDE0103 physical sciencesFOS: MathematicsMathematics (all)0101 mathematicspopp measureMathematicsosittaisdifferentiaaliyhtälötsubelliptic PDESmoothnessQuasi-conformal mapApplied MathematicsHarmonic coordinates; Liouville Theorem; Quasi-conformal maps; Regularity for p-harmonic functions; Sub-Riemannian geometry; Subelliptic PDE; Mathematics (all); Applied Mathematicsta111Harmonic coordinate010102 general mathematics53C17 35H20 58C25Metric Geometry (math.MG)16. Peace & justiceregularity for p-harmonic functionsSub-Riemannian geometrysub-Riemannian geometryDifferential Geometry (math.DG)quasi-conformal mapsRegularity for p-harmonic functionsharmonic coordinates010307 mathematical physicsMathematics::Differential GeometrymonistotLiouville theoremAnalysis of PDEs (math.AP)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-03-17 |