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Isoperimetric Regions in Gauss Sectors

Vol: 8, Issue: 1
2017
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Article Description

We consider the free boundary isoperimetric problem in sectors of the Gauss plane. The solution is not always a circular arc as in sectors of the Euclidean plane. We prove that the solution is sometimes a ray and we conjecture that the solution is sometimes a "rounded n-gon" which we discovered computationally using Mathematica.

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