Double Bubbles on the Real Line with Log-Convex Density
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝN is the standard double bubble. We seek the optimal double bubble in ℝN with density, which we assume to be strictly log-convex. For N = 1 we show that the solution is sometimes tw...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-06-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.1515/agms-2018-0004 |
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doaj-0e22d3c033cb4dfd8a01795b1033afc12021-09-06T19:39:45ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742018-06-0161648810.1515/agms-2018-0004agms-2018-0004Double Bubbles on the Real Line with Log-Convex DensityBongiovanni Eliot0Di Giosia Leonardo1Diaz Alejandro2Habib Jahangir3Kakkar Arjun4Kenigsberg Lea5Pittman Dylanger6Sothanaphan Nat7Zhu Weitao8Michigan State University, USARice University, Houston, Texas, USAUniversity of Maryland, College Park, USAWilliams College, Williamstown, USAWilliams College, Williamstown, USAColumbia University in the City of New York, USAWilliams College, Williamstown, USAMassachusetts Institute of Technology, Cambridge, MA 02139, USAWilliams College, Williamstown, USAThe classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝN is the standard double bubble. We seek the optimal double bubble in ℝN with density, which we assume to be strictly log-convex. For N = 1 we show that the solution is sometimes two contiguous intervals and sometimes three contiguous intervals. In higher dimensions we think that the solution is sometimes a standard double bubble and sometimes concentric spheres (e.g. for one volume small and the other large).https://doi.org/10.1515/agms-2018-0004double bubbledensityisoperimetric49q10 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Bongiovanni Eliot Di Giosia Leonardo Diaz Alejandro Habib Jahangir Kakkar Arjun Kenigsberg Lea Pittman Dylanger Sothanaphan Nat Zhu Weitao |
| spellingShingle |
Bongiovanni Eliot Di Giosia Leonardo Diaz Alejandro Habib Jahangir Kakkar Arjun Kenigsberg Lea Pittman Dylanger Sothanaphan Nat Zhu Weitao Double Bubbles on the Real Line with Log-Convex Density Analysis and Geometry in Metric Spaces double bubble density isoperimetric 49q10 |
| author_facet |
Bongiovanni Eliot Di Giosia Leonardo Diaz Alejandro Habib Jahangir Kakkar Arjun Kenigsberg Lea Pittman Dylanger Sothanaphan Nat Zhu Weitao |
| author_sort |
Bongiovanni Eliot |
| title |
Double Bubbles on the Real Line with Log-Convex Density |
| title_short |
Double Bubbles on the Real Line with Log-Convex Density |
| title_full |
Double Bubbles on the Real Line with Log-Convex Density |
| title_fullStr |
Double Bubbles on the Real Line with Log-Convex Density |
| title_full_unstemmed |
Double Bubbles on the Real Line with Log-Convex Density |
| title_sort |
double bubbles on the real line with log-convex density |
| publisher |
De Gruyter |
| series |
Analysis and Geometry in Metric Spaces |
| issn |
2299-3274 |
| publishDate |
2018-06-01 |
| description |
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝN is the standard double bubble. We seek the optimal double bubble in ℝN with density, which we assume to be strictly log-convex. For N = 1 we show that the solution is sometimes two contiguous intervals and sometimes three contiguous intervals. In higher dimensions we think that the solution is sometimes a standard double bubble and sometimes concentric spheres (e.g. for one volume small and the other large). |
| topic |
double bubble density isoperimetric 49q10 |
| url |
https://doi.org/10.1515/agms-2018-0004 |
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