THE SHORTEST ENCLOSURE OF THREE CONNECTED AREAS IN ℝ2

Christopher Cox; Lisa Harrison; Michael Hutchings; Susan Kim; Janette Light; Andrew Mauer; Meg Tilton; Frank Morgan

doi:10.2307/44152491

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Home > Journals > Real Anal. Exchange > Volume 20 > Issue 1 > Article

1994/1995 THE SHORTEST ENCLOSURE OF THREE CONNECTED AREAS IN

{\mathbb{R}^2

Christopher Cox, Lisa Harrison, Michael Hutchings, Susan Kim, Janette Light, Andrew Mauer, Meg Tilton, Frank Morgan

Real Anal. Exchange 20(1): 313-335 (1994/1995). DOI: 10.2307/44152491

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Abstract

We show that the “standard triple bubble” is the shortest way to enclose and separate three areas in ${\mathbb{R}^2$ , assuming that the enclosed regions and the exterior region are connected.

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Christopher Cox. Lisa Harrison. Michael Hutchings. Susan Kim. Janette Light. Andrew Mauer. Meg Tilton. Frank Morgan. "THE SHORTEST ENCLOSURE OF THREE CONNECTED AREAS IN ${\mathbb{R}^2$ ." Real Anal. Exchange 20 (1) 313 - 335, 1994/1995. https://doi.org/10.2307/44152491

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Published: 1994/1995

First available in Project Euclid: 30 March 2022

Digital Object Identifier: 10.2307/44152491

Subjects:

Primary: 28A75 , 49Q10 , 52A38

Keywords: isoperimetric problems , soap bubble clusters

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Real Anal. Exchange

Vol.20 • No. 1 • 1994/1995

Michigan State University Press

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Christopher Cox, Lisa Harrison, Michael Hutchings, Susan Kim, Janette Light, Andrew Mauer, Meg Tilton, Frank Morgan "THE SHORTEST ENCLOSURE OF THREE CONNECTED AREAS IN

{\mathbb{R}^2

," Real Analysis Exchange, Real Anal. Exchange 20(1), 313-335, (1994/1995)

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