Delone sets that are not rectifiable under Lipschitz co-uniformly continuous bijections

2021/05/02 by Rodolfo Viera, Viera, Rodolfo
Computer Science · #30L05 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2105.00515

openalex publication_date 2021/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that there exist Delone sets in ℝ^d, d ≥ 2, which cannot be mapped onto the standard lattice ℤ^d by Lipschitz co-uniformly continuous bijections satisfying an asymptotic control on the lower distortion. The impossibility of the unrectifiability crucially uses ideas of Lipschitz regular maps recently introduced by M. Dymond, V. Kaluža and E. Kopecká.

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