English

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

Analysis of PDEs 2023-09-21 v1 Differential Geometry

Abstract

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

Keywords

Cite

@article{arxiv.2309.11264,
  title  = {$\varepsilon$-approximability and Quantitative Fatou Theorem on Riemannian Manifolds},
  author = {Marcin Gryszówka},
  journal= {arXiv preprint arXiv:2309.11264},
  year   = {2023}
}