BCAM Seminar Isoperimetric inequality in gauss space and its stability

In this talk we will discuss the isoperimetric problem in the Gauss space, underlining the common points and the differences with the Euclidean case. Using Ehrhard symmetrization (the Gaussian version of the usual Schwarz symmetrization), we will give a short proof of the optimality of the half-spaces, and then we will briefly describe the strategy to reach a stability version of this result.