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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Conformality And Q-Harmonicity In Sub-Riemannian Manifolds, Luca Capogna, Giovanna Citti, Enrico Le Donne, Alessandro Ottazzi
Conformality And Q-Harmonicity In Sub-Riemannian Manifolds, Luca Capogna, Giovanna Citti, Enrico Le Donne, Alessandro Ottazzi
Mathematics Sciences: Faculty Publications
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].
Strong Comparison Principle For P-Harmonic Functions In Carnot-Caratheodory Spaces, Luca Capogna, Xiaodan Zhou
Strong Comparison Principle For P-Harmonic Functions In Carnot-Caratheodory Spaces, Luca Capogna, Xiaodan Zhou
Mathematics Sciences: Faculty Publications
We extend Bony’s propagation of support argument to C1 solutions of the nonhomogeneous subelliptic p-Laplacian associated to a system of smooth vector fields satisfying Hörmander’s finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that generalize results of Tolksdorf.
Regularity For Subelliptic Pde Through Uniform Estimates In Multi-Scale Geometries, Luca Capogna, Giovanna Citti
Regularity For Subelliptic Pde Through Uniform Estimates In Multi-Scale Geometries, Luca Capogna, Giovanna Citti
Mathematics Sciences: Faculty Publications
We aim at reviewing and extending a number of recent results addressing stability of certain geometric and analytic estimates in the Riemannian approximation of subRiemannian structures. In particular we extend the recent work of the the authors with Rea (Math Ann 357(3):1175–1198, 2013) and Manfredini (Anal Geom Metric Spaces 1:255–275, 2013) concerning stability of doubling properties, Poincare’ inequalities, Gaussian estimates on heat kernels and Schauder estimates from the Carnot group setting to the general case of Hörmander vector fields.