Calculus of Variations and Geometric Measure Theory

A. Figalli

Quantitative isoperimetric inequalities, with applications to the stability of liquid drops and crystals

created by figalli on 02 Jul 2010
modified on 09 Feb 2013



Inserted: 2 jul 2010
Last Updated: 9 feb 2013

Journal: Contemp. Math.
Year: 2010


Recently, in collaboration with Maggi and Pratelli, the author proved a sharp quantitative version of the anisotropic isoperimetric inequality using optimal transportation. Subsequently, this result has been applied by the author and Maggi to study the stability of the shape of small liquid drops and crystals under the action of an exterior potential. This note is a review of these results.