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Besicovitch-Morse type covering lemmas in metric spaces (2107.01342v2)
Published 3 Jul 2021 in math.CA and math.DG
Abstract: The aims of this article is to generalize some useful Besicovitch-Morse type covering lemmas in complete Riemannian manifolds and try to find more spaces such that the so-called BCP and WBCP are equivalent while these two properties are weaker and still useful. We also get interest in the best constants of Besicovitch-type covering properties in Euclidean spaces and sorted out the best results of related problems before giving a new proof of Besicovitch covering theorem in the one-dimensional case.