ε-approximability and Quantitative Fatou Theorem on Riemannian Manifolds

2023/09/20 by Gryszówka, Marcin
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.11264

Abstract

We prove the Quantitative Fatou Theorem for Lipschitz domains on complete Riemannian manifolds. This requires extending the ε-approximation lemma to the manifold setting. Our studies apply to harmonic functions, as well as to a class of A-harmonic functions on manifolds. The presented results extend works by Dahlberg, Garnett, Bortz and Hofmann.

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