A Selection Principle for the Sharp Quantitative Isoperimetric Inequality

Details A Selection Principle for the Sharp Quantitative Isoperimetric Inequality A Selection Principle for the Sharp Quantitative Isoperimetric Inequality

2010-07-22

arxiv.org/abs/1007.3899v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

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

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