The Jung inequality for transfinite diameters

A. Yu Solynin

doi:10.1007/BF02111333

The Jung inequality for transfinite diameters

A. Yu Solynin

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

The following analog of Jung's theorem on coverings of a compact disk is proved. For each continuum E ⊂ C, there exists a unique covering E of the disk with minimal radius R(E), and here R(E) ≤ 2d(E), where d(E) is the transfinite diameter of E; we have R(e)=2d(E) only in the case of a line segment. Applications of this result are given.

Original language	English
Pages (from-to)	2147-2151
Number of pages	5
Journal	Journal of Mathematical Sciences
Volume	70
Issue number	6
DOIs	https://doi.org/10.1007/BF02111333
State	Published - Aug 1994

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10.1007/BF02111333

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title = "The Jung inequality for transfinite diameters",

abstract = "The following analog of Jung's theorem on coverings of a compact disk is proved. For each continuum E ⊂ C, there exists a unique covering E of the disk with minimal radius R(E), and here R(E) ≤ 2d(E), where d(E) is the transfinite diameter of E; we have R(e)=2d(E) only in the case of a line segment. Applications of this result are given.",

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AB - The following analog of Jung's theorem on coverings of a compact disk is proved. For each continuum E ⊂ C, there exists a unique covering E of the disk with minimal radius R(E), and here R(E) ≤ 2d(E), where d(E) is the transfinite diameter of E; we have R(e)=2d(E) only in the case of a line segment. Applications of this result are given.

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SP - 2147

EP - 2151

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

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The Jung inequality for transfinite diameters

Abstract

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