Isoperimetric Inequality in Euclidean Space

Course : Isoperimetric Inequality in Euclidean Space [ July 29 to August 02, 2024]

Abstract: In this mini course, I am planning to prove the Isoperimetric inequality. This has many applications and I try to bring Polya-Szego inequality related to Symmetrization. This is a very useful theorem in PDE. In order to prove the Isoperimetric inequality, one uses integration by parts, Besicovitch covering lemma and Brunn-Minkowski inequality. If time permits, I will state some interesting problems on its own. 

Instructor: Adi Adimurthi, TIFR CAM

Topics: 

1. Measure theoretic inequalities

2. Besicovitch covering lemma and its consequences

3. Brunn-Minkowski inequality

4. Isoprimetric inequality

Background required: Those who have a good background in real analysis including n-dimensional measure theory (M.Sc. first year level), will be able to follow these lectures. PhD Scholars and young faculty members are also eligible to apply. 

Selected candidates are listed below.