Double Bubbles on the Real Line with Log-Convex Density
| Autor: | Bongiovanni, Eliot, Di Giosia, Leonardo, Diaz, Alejandro, Habib, Jahangir, Kakkar, Arjun, Kenigsberg, Lea, Pittman, Dylanger, Sothanaphan, Nat, Zhu, Weitao |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Anal. Geom. Metric Spaces 6 (2018) 64-88 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1515/agms-2018-0004 |
| Popis: | The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in $\mathbb{R}^N$ is the standard double bubble. We seek the optimal double bubble in $\mathbb{R}^N$ 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). Comment: 47 pages, 10 figures |
| Databáze: | arXiv |
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