The aim of the course is to give a self contained introduction, at the level of a graduate course, to the stability of the isoperimetric inequality and other related geometric and functional inequality such as the Sobolev inequality, the Faber-Krahn and the Brunn-Minkowski inequality.
Lecture 1: I will introduce some basic notions of the theory of sets of ignite perimeter and of geometric measure theory.
Nicola Fusco (born August 14, 1956 in Napoli) is an Italian mathematician mainly known for his contributions to the fields of calculus of variations, regularity theory of partial differential equations, and the theory of symmetrization. He is currently professor at the Università di Napoli "Federico II". Fusco also taught and conducted research at the Australian National University at Canberra, the Carnegie Mellon University at Pittsburgh and at the University of Florence.
Fusco won the 1994 edition of the Caccioppoli Prize of the Italian Mathematical Union, and, in 2010, the Tartufari Prize from the Accademia Nazionale dei Lincei. In 2008 he was an invited speaker at European Congress of Mathematics and in 2010 he was invited speaker at the International Congress of Mathematicians on the topic of "Partial Differential Equations."
From 2010 he is a corresponding member of Accademia Nazionale dei Lincei, the Italian National Academy. From 2013 to 2016, appointed as FiDiPro professor at the University of Jyvaskyla in Finland.