Resumen de la charla: : The isoperimetric problem - first recorded in Ancient Greece -states that among all sets of fixed volume, the ball has minimal perimeter. More recently, quantitative versions of this inequality have been shown that compare suitable distances of a set to a ball of the same volume by the isoperimetric deficit. In this talk, I will give a brief overview of the different techniques to prove the isoperimetric inequality and its stability,  and will discuss a novel argument to derive a sharp quantitative form, which in particular implies all previously known versions. The argument is based solely on a notion of "quantitative calibrations" from which one may define a coercive relative energy, penalizing the difference between two interfaces in a sharp way. This is joint work with Sebastian Hensel.

Lugar: Aula Especializada del CIMPA
Organiza: Centro de Investigación en Matemáticas Pura y Aplicada (CIMPA)
Participantes:

Tim Laux, Ph. D., Heidelberg University