0000000000814650

AUTHOR

Giovanna Citti

showing 2 related works from this author

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

2016

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.

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)
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Harnack estimates for degenerate parabolic equations modeled on the subelliptic $p-$Laplacian

2014

Abstract We establish a Harnack inequality for a class of quasi-linear PDE modeled on the prototype ∂ t u = − ∑ i = 1 m X i ⁎ ( | X u | p − 2 X i u ) where p ⩾ 2 , X = ( X 1 , … , X m ) is a system of Lipschitz vector fields defined on a smooth manifold M endowed with a Borel measure μ, and X i ⁎ denotes the adjoint of X i with respect to μ. Our estimates are derived assuming that (i) the control distance d generated by X induces the same topology on M ; (ii) a doubling condition for the μ-measure of d-metric balls; and (iii) the validity of a Poincare inequality involving X and μ. Our results extend the recent work in [16] , [36] , to a more general setting including the model cases of (1)…

Mathematics - Differential GeometryPure mathematicsGeneral MathematicsMathematics::Analysis of PDEsPoincaré inequalityVolume formsymbols.namesakeMathematics - Analysis of PDEsMathematics - Metric GeometryFOS: MathematicsP-LAPLACIAN OPERATORBorel measureRicci curvatureMathematicsHarnack's inequalityMatematikLebesgue measureta111HORMANDER VECTOR FIELDSMetric Geometry (math.MG)Lipschitz continuity35H20Differential Geometry (math.DG)p-LaplaciansymbolsHARNACK INEQUALITYMathematicsAnalysis of PDEs (math.AP)
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