Isoperimetric Regions in Gauss SectorsThere is also another paper that should be published sometime soon in a different journal.
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.
3 hours ago