A1 Journal article (refereed)
Symmetry of minimizers of a Gaussian isoperimetric problem (2020)
Barchiesi, M., & Julin, V. (2020). Symmetry of minimizers of a Gaussian isoperimetric problem. Probability Theory and Related Fields, 177(1-2), 217-256. https://doi.org/10.1007/s00440-019-00947-9
JYU authors or editors
Publication details
All authors or editors: Barchiesi, Marco; Julin, Vesa
Journal or series: Probability Theory and Related Fields
ISSN: 0178-8051
eISSN: 1432-2064
Publication year: 2020
Volume: 177
Issue number: 1-2
Pages range: 217-256
Publisher: Springer
Publication country: Germany
Publication language: Finnish
DOI: https://doi.org/10.1007/s00440-019-00947-9
Publication open access: Not open
Publication channel open access:
Web address of parallel published publication (pre-print): https://arxiv.org/abs/1805.03161
Abstract
We study an isoperimetric problem described by a functional that consists of the standard Gaussian perimeter and the norm of the barycenter. The second term is in competition with the perimeter, balancing the mass with respect to the origin, and because of that the solution is not always the half-space. We characterize all the minimizers of this functional, when the volume is close to one, by proving that the minimizer is either the half-space or the symmetric strip, depending on the strength of the barycenter term. As a corollary, we obtain that the symmetric strip is the solution of the Gaussian isoperimetric problem among symmetric sets when the volume is close to one. As another corollary we obtain the optimal constant in the quantitative Gaussian isoperimetric inequality.
Free keywords: isoperimetric problems; Gaussian problem
Contributing organizations
Related projects
- Variational problems of isoperimetric type. Stability and Geometric flows (research costs)
- Julin, Vesa
- Research Council of Finland
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 3