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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
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Abstract |
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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. |
Keywords
isoperimetric, Gaussian
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Mathematical Subject Classification 2010
Primary: 49Q10, 53A10
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Milestones
Received: 1 August 2016
Accepted: 21 August 2016
Published: 15 January 2018
Communicated by Gaven Martin
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Authors |
| John Berry | |
| Department of Mathematics and
Statistics Williams College Williamstown, MA United States |
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| Matthew Dannenberg | |
| Department of Mathematics Harvey Mudd College Claremont, CA United States |
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| Jason Liang | |
| Department of Mathematics University of Chicago Chicago, IL United States |
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| Yingyi Zeng | |
| Department of Mathematics and
Computer Science St. Mary’s College of Maryland St. Mary’s City, MD United States |
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