Michael Dymond

activity

20242026

collaborators

4 papers

math.MG2026

Non-rectifiable Delone sets under pointwise co-Lipschitz bijections

Ashwin Bhat, Michael Dymond

For each $d \in N_{\geq 2}$ we construct a Delone set $Y$ in $R^{d}$ for which every Lipschitz bijection from $Y$ to $Z^{d}$ has a very irregular inverse. For example, the inverse…

math.MG2025

Extending Bilipschitz Mappings between Separated Nets

Michael Dymond, Vojtěch Kaluža

We provide a new characterisation of the decades old open problem of extending bilipschitz mappings given on a Euclidean separated net. In particular, this allows for the complete…

math.MG2025

Fast repetitivity in non-rectifiable Delone sets

Ashwin Bhat, Michael Dymond

We present a construction of non-rectifiable, repetitive Delone sets in every Euclidean space $R^{d}$ with $d \geq 2$ . We further obtain a close to optimal repetitivity func…

math.MG2024

Planar Bilipschitz Extension from Separated Nets

Michael Dymond, Vojtěch Kaluža

We prove that every $L$ -bilipschitz mapping $Z^{2} \to R^{2}$ can be extended to a $C (L)$ -bilipschitz mapping $R^{2} \to R^{2}$ and provide a polynomial upp…