Work

Double Bubbles on the Real Line with Log-Convex Density

Year: 2018

Type: article

Abstract: 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).

Source: Analysis and Geometry in Metric Spaces

DOI: 10.1515/agms-2018-0004

Authors: Eliot Bongiovanni, Leonardo Di Giosia, Alejandro Diaz, Jahangir Habib, Arjun Kakkar, Lea Kenigsberg, Dylanger Pittman, Nat Sothanaphan, Weitao Zhu

Institutions: Michigan State University, Rice University, University of Maryland, College Park, Williams College, Columbia University, Massachusetts Institute of Technology

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,187

Funders: National Science Foundation, Williams College, Massachusetts Institute of Technology, Michigan State University, Mathematical Association of America, Stony Brook University, College of Engineering, Michigan State University

OpenAlex ID: W2743385587

FWCI: 0.695

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Cited by: 5

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