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 a paper by Fusco, Maggi and Pratelli (Ann. Math. 2008), for a class of not necessarily convex sets called sets with positive reach. Our work is based on geometrical results on sets with positive reach, obtained using methods of both nonsmooth analysis and geometric measure theory.
Quantitative isoperimetric inequalities for a class of nonconvex sets
COLOMBO, GIOVANNI;NGUYEN, TIEN KHAI
2010
Abstract
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 a paper by Fusco, Maggi and Pratelli (Ann. Math. 2008), for a class of not necessarily convex sets called sets with positive reach. Our work is based on geometrical results on sets with positive reach, obtained using methods of both nonsmooth analysis and geometric measure theory.
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