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The Isoperimetric Inequality for Curves with Self-Intersections

Published online by Cambridge University Press:  20 November 2018

Andrew Vogt
Andrew Vogt*
Affiliation:
Department of Mathematics, Georgetown University Washington, D.C. 20057, U.S.A.
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Banchoff and Pohl [3] have proved the following generalization of the isoperimetric inequality.

Theorem. If γ is a closed, not necessarily simple, planar curve of length L, and w(p) is the winding number of a variable point p with respect to γ, then

1

with equality holding if and only if γ is a circle traversed a finite number of times in the same sense.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 2 , 01 June 1981 , pp. 161 - 167
Copyright
Copyright © Canadian Mathematical Society 1981

References

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