Geodesic
The Isoperimetric Inequality for Curves with Self-Intersections
Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 161-167

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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. 
Vogt, Andrew. The Isoperimetric Inequality for Curves with Self-Intersections. Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 161-167. doi: 10.4153/CMB-1981-026-8
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     title = {The {Isoperimetric} {Inequality} for {Curves} with {Self-Intersections}},
     journal = {Canadian mathematical bulletin},
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     year = {1981},
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     number = {2},
     doi = {10.4153/CMB-1981-026-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-026-8/}
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