Finite trees inside thin subsets of \Bbb R^d

2019/03/06 by Alex Iosevich, Iosevich, Alex, Krystal Taylor +1
Computer Science · Mathematics · #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.CA #msc:42B

paper · pdf · doi:10.48550/arxiv.1903.02662

arxiv created 2019/03/06 · arxiv updated 2019/03/08

Abstract

Bennett, Iosevich and Taylor proved that compact subsets of \Bbb R^d, d ≥ 2, of Hausdorff dimensions greater than (d+1)/(2) contain chains of arbitrary length with gaps in a non-trivial interval. In this paper we generalize this result to arbitrary tree configurations.

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