Best constants for the isoperimetric inequality in quantitative form
Marco Cicalese, Gian Paolo Leonardi (2013)
Journal of the European Mathematical Society
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We prove some results in the context of isoperimetric inequalities with quantitative terms. In the -dimensional case, our main contribution is a method for determining the optimal coefficients in the inequality , valid for each Borel set with positive and finite area, with and being, respectively, the and the of . In dimensions, besides proving existence and regularity properties of minimizers for a wide class of including the lower semicontinuous extension of , we...