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Calibrations and isoperimetric profiles

2007

We equip many noncompact nonsimply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly nongeneric property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new results on the profile of surfaces of revolution and some hardware know-how.