Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies

@article{Figalli2015IsoperimetryAS,
  title={Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies},
  author={Alessio Figalli and Nicola Fusco and Francesco Maggi and Vincent Millot and Massimiliano Morini},
  journal={Communications in Mathematical Physics},
  year={2015},
  volume={336},
  pages={441-507}
}
We obtain a sharp quantitative isoperimetric inequality for nonlocal s-perimeters, uniform with respect to s bounded away from 0. This allows us to address local and global minimality properties of balls with respect to the volume-constrained minimization of a free energy consisting of a nonlocal s-perimeter plus a non-local repulsive interaction term. In the particular case s = 1, the s-perimeter coincides with the classical perimeter, and our results improve the ones of Knuepfer and Muratov… 

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