Local minimality of the ball for the Gaussian perimeter

Abstract

AbstractWe prove that balls centered at the origin and with small radius are stable local minimizers of the Gaussian perimeter among all symmetric sets. Precisely, using the second variation of the Gaussian perimeter, we show that if the radius is smaller than{\sqrt{n+1}}, then the ball is a local minimizer, while if it is larger, the ball is not a local minimizer.