The quantitative isoperimetric inequality: A calibration argumentOberseminar Analysis

Wednesday Mar 4, 2026, 2:15 PM → 4:00 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Abstract: I discuss a novel argument to derive a quantitative form of  the classical isoperimetric inequality, which in particular implies 
all previously known versions. The argument is based solely upon a notion of "quantitative calibrations" from which one may define a 
coercive relative energy, penalizing the difference between two  interfaces in a, e.g., tilt-excess type way. I give some insights how 
this allows to prove the following local result: Let $F \subset \mathbb{R}^d$ a set of finite perimeter with same barycenter and 
volume as the unit ball $B_1(0)$, then one can bound from below the energy gap $Per(F) - Per(B_1(0))$ by the associated relative energy 
(to be defined in the talk) provided this relative energy is sufficiently small. Based on this local version, we then deduce by a 
simple compactness argument a corresponding result for arbitrary admissible competitors. This is joint work with Tim Laux.