Disks in Curves of Bounded Convex Curvature

Anders Aamand; Mikkel Abrahamsen; Mikkel Thorup

doi:10.1080/00029890.2020.1752602

Disks in Curves of Bounded Convex Curvature

Anders Aamand, Mikkel Abrahamsen^*, Mikkel Thorup

^*Corresponding author for this work

Algorithms and Complexity

Research output: Contribution to journal › Journal article › Research › peer-review

3 Citations (Scopus)

20 Downloads (Pure)

Abstract

We say that a simple, closed curve γ in the plane has bounded convex curvature if for every point x on γ, there is an open unit disk U_x and (Formula presented.) such that (Formula presented.) and (Formula presented.). We prove that the interior of every curve of bounded convex curvature contains an open unit disk.

Original language	English
Journal	American Mathematical Monthly
Volume	127
Issue number	7
Pages (from-to)	579-593
Number of pages	15
ISSN	0002-9890
DOIs	https://doi.org/10.1080/00029890.2020.1752602
Publication status	Published - 2020

Keywords

MSC: Primary 51M04
Secondary 53A04

Access to Document

10.1080/00029890.2020.1752602

FulltextAccepted author manuscript, 3.03 MBLicence: CC BY-NC-ND

Cite this

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abstract = "We say that a simple, closed curve γ in the plane has bounded convex curvature if for every point x on γ, there is an open unit disk Ux and (Formula presented.) such that (Formula presented.) and (Formula presented.). We prove that the interior of every curve of bounded convex curvature contains an open unit disk.",

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AU - Abrahamsen, Mikkel

AU - Thorup, Mikkel

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AB - We say that a simple, closed curve γ in the plane has bounded convex curvature if for every point x on γ, there is an open unit disk Ux and (Formula presented.) such that (Formula presented.) and (Formula presented.). We prove that the interior of every curve of bounded convex curvature contains an open unit disk.

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KW - Secondary 53A04

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DO - 10.1080/00029890.2020.1752602

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EP - 593

JO - American Mathematical Monthly

JF - American Mathematical Monthly

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