Vol. 11, No. 4, 2018

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The isoperimetric problem in the plane with the sum of two Gaussian densities

John Berry, Matthew Dannenberg, Jason Liang and Yingyi Zeng

Vol. 11 (2018), No. 4, 549–567
Abstract

We consider the isoperimetric problem for the sum of two Gaussian densities in the line and the plane. We prove that the double Gaussian isoperimetric regions in the line are rays and that if the double Gaussian isoperimetric regions in the plane are half-spaces, then they must be bounded by vertical lines.

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Keywords
isoperimetric, Gaussian
Mathematical Subject Classification 2010
Primary: 49Q10, 53A10
Milestones
Received: 1 August 2016
Accepted: 21 August 2016
Published: 15 January 2018

Communicated by Gaven Martin
Authors
John Berry
Department of Mathematics and Statistics
Williams College
Williamstown, MA
United States
Matthew Dannenberg
Department of Mathematics
Harvey Mudd College
Claremont, CA
United States
Jason Liang
Department of Mathematics
University of Chicago
Chicago, IL
United States
Yingyi Zeng
Department of Mathematics and Computer Science
St. Mary’s College of Maryland
St. Mary’s City, MD
United States