paper

$\varepsilon$-approximability and Quantitative Fatou Theorem on Riemannian Manifolds

Marcin Gryszówka

$\varepsilon$-approximability and Quantitative Fatou Theorem on Riemannian Manifolds

Name: $\varepsilon$-approximability and Quantitative Fatou Theorem on Riemannian Manifolds
Author: Marcin Gryszówka

Marcin Gryszówka

paper2023-09-20English

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Description

We prove the Quantitative Fatou Theorem for Lipschitz domains on complete Riemannian manifolds. This requires extending the $\varepsilon$-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.