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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

Covered by SCOPUS, Web of Science - Science Citation Index Expanded, MathSciNet, and Zentralblatt Math (zbMATH)

IMPACT FACTOR 2018: 0.536

CiteScore 2018: 0.83

SCImago Journal Rank (SJR) 2018: 1.041
Source Normalized Impact per Paper (SNIP) 2018: 0.801

Mathematical Citation Quotient (MCQ) 2018: 0.83

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Double Bubbles on the Real Line with Log-Convex Density

Eliot Bongiovanni / Leonardo Di Giosia / Alejandro Diaz / Jahangir Habib / Arjun Kakkar / Lea Kenigsberg / Dylanger Pittman / Nat Sothanaphan / Weitao Zhu
Published Online: 2018-06-15 | DOI: https://doi.org/10.1515/agms-2018-0004


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).

Keywords : double bubble; density; isoperimetric

MSC 2010: 49Q10


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About the article

Received: 2017-09-20

Revised: 2018-03-30

Accepted: 2018-05-02

Published Online: 2018-06-15

Citation Information: Analysis and Geometry in Metric Spaces, Volume 6, Issue 1, Pages 64–88, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2018-0004.

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© 2018 Nat Sothanaphan, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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