Besicovitch-Morse type covering lemmas in metric spaces

2021/07/03 by Tong Zhang, Zhang, Tong
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Fixed Point Theorems Analysis #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2107.01342

openalex publication_date 2021/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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