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Local minimality of the ball for the Gaussian perimeter

  • Domenico Angelo La Manna EMAIL logo
Veröffentlicht/Copyright: 7. Juli 2017

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.

MSC 2010: 49Q20; 60E15

Communicated by Frank Duzaar


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Received: 2017-02-17
Revised: 2017-05-25
Accepted: 2017-06-28
Published Online: 2017-07-07
Published in Print: 2019-04-01

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