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An isoperimetric inequality for the thread problem

Published online by Cambridge University Press:  17 April 2009

Frank Morgan
Frank Morgan
Affiliation:
Department of Mathematics, Williams College, Williamstown, MA 01267United States of America
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Given a fixed curve C0 in Rn of length L0 and a variable curve C of fixed length L ≤ L0, the thread problem seeks a least-area surface bounded by C0 + C. We show that an extreme case is a circular arc and its chord. We provide some counterexamples and generalisations to higher dimensions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 489 - 495
Copyright
Copyright © Australian Mathematical Society 1997

References

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