Bulletin of the London Mathematical Society



NOTES AND PAPERS

AN ISOPERIMETRIC RESULT FOR THE GAUSSIAN MEASURE AND UNCONDITIONAL SETS


F. BARTHE a1 1
a1 CNRS, Université de Marne-la-Vallée, Équipe d'Analyse et Mathématiques Appliquées, ESA 8050, Boulevard Descartes, Cité Descartes, Champs sur Marne, 77454 Marne la Vallée Cedex 2, France; barthe@math.univ-mlv.fr

Abstract

The paper studies an isoperimetric problem for the Gaussian measure and coordinatewise symmetric sets. The notion of boundary measure corresponding to the uniform enlargement is considered, and it is proved that symmetric strips or their complements have minimal boundary measure.

(Received March 17 2000)
(Revised September 12 2000)



Footnotes

1 Partially supported by a grant of the Ostrowski foundation.