2013/02/24 by Camille Petit, Petit, Camille
Mathematics · #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Probability (math.PR) #math.CA #math.MG #math.PR
paper · pdf · doi:10.48550/arxiv.1302.5940
arxiv created 2013/02/24 · openalex publication_date 2013/02/24 · arxiv updated 2013/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a complete simply connected manifold which is in addition Gromov hyperbolic, coercive and roughly starlike. For a given harmonic function on M, a local Fatou Theorem and a pointwise criteria of non-tangential convergence coming from the density of energy are shown: at almost all points of the boundary, the harmonic function converges non-tangentially if and only if the supremum of the density of energy is finite. As an application of these results, a Calderón-Stein Theorem is proved, that is, the non-tangential properties of convergence, boundedness and finiteness of energy are equivalent at almost every point of the boundary.