We 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 √ n + 1, then the ball is a local minimizer, while if it is larger, the ball is not a local minimizer.
Local minimality of the ball for the Gaussian perimeter / La Manna, D. A.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 12:2(2019), pp. 193-210. [10.1515/acv-2017-0007]
Local minimality of the ball for the Gaussian perimeter
La Manna D. A.
2019
Abstract
We 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 √ n + 1, then the ball is a local minimizer, while if it is larger, the ball is not a local minimizer.File in questo prodotto:
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