Quantitative isoperimetric inequalities for a class of nonconvex sets

Colombo, Giovanni; Khai Nguyen
January 2010
Calculus of Variations & Partial Differential Equations;Jan2010, Vol. 37 Issue 1/2, p141
Academic Journal
Quantitative versions (i.e., taking into account a suitable �distance� of a set from being a sphere) of the isoperimetric inequality are obtained, in the spirit of Fuglede (Trans Am Math Soc 314:619�638, 1989) and Fusco et al. (Ann Math 168:941�980, 2008) for a class of not necessarily convex sets called f-convex sets. Our work is based on geometrical results on f-convex sets, obtained using methods of both nonsmooth analysis and geometric measure theory.


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