关于二义轨迹的一个旧定理Erdős

IF 0.4 4区数学 Q4 MATHEMATICS

Colloquium Mathematicum Pub Date : 2022-01-01 DOI:10.4064/cm8460-9-2021

P. Hajłasz

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引用次数: 6

摘要

． Erdős在1946年证明了如果集合E∧R n是闭的非空的，那么这个集合(称为二义轨迹或中轴线)在R n中的点具有E中最近的点不是唯一的性质，可以被可数的多个有限(n−1)维测度的曲面所覆盖。我们从凸性和c2正则性两个方面得到了一个新的正则性结果，从而对结果进行了改进。

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On an old theorem of Erdős about ambiguous locus

. Erdős proved in 1946 that if a set E ⊂ R n is closed and non-empty, then the set, called ambiguous locus or medial axis, of points in R n with the property that the nearest point in E is not unique, can be covered by countably many surfaces, each of ﬁnite ( n − 1) -dimensional measure. We improve the result by obtaining a new regularity result for these surfaces in terms of convexity and C 2 regularity.

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来源期刊

Colloquium Mathematicum MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics. Two issues constitute a volume, and at least four volumes are published each year.