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We introduce a new variational method for the study of stability in theisoperimetric inequality. The method is quite general as it relies on apenalization technique combined with the regularity theory for quasiminimizersof the perimeter. Two applications are presented. First we give a new proof ofthe sharp quantitative isoperimetric inequality in $R^n$. Second we positivelyanswer to a conjecture by Hall concerning the best constant for thequantitative isoperimetric inequality in $R^2$ in the small asymmetry regime.

A Selection Principle for the Sharp Quantitative Isoperimetric Inequality