逐点共Lipschitz双射下的不可求长Delone集
Non-rectifiable Delone sets under pointwise co-Lipschitz bijections
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中文总结 AI 辅助
针对d≥2的情况，构造了ℝᵈ中一类Delone集，其到ℤᵈ的Lipschitz双射的逆映射极不规则，还阐明了Delone集双射正则性概念间的关系。
中文摘要 AI 辅助
对每个整数d≥2，我们在ℝᵈ中构造一个Delone集Y，使得从Y到ℤᵈ的每个Lipschitz双射都具有极不规则的逆映射，例如逆映射甚至在单个点处就不满足Lipschitz条件。此外，我们阐明了文献中研究的Delone集之间双射的若干正则性概念的关系。
英文摘要
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 fails to be Lipschitz, even at just a single point. Further, we clarify the relationship between several notions of regularity for bijections between Delone sets, studied in the literature.
