Abstract We study the n -bubble problem on $$\mathbb {R}^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> </mml:math> with a prescribed density function f that is even, radially increasing, and satisfies a log-concavity requirement. Under these conditions, we find that isoperimetric solutions can be identified for an arbitrary number of regions, and that these solutions have a well-understood and regular structure. This generalizes recent work done on the density function $$|x |^p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>x</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:msup> </mml:math> and stands in contrast to log-convex density functions which are known to have no such regular structure.

John Ross

Annals of Global Analysis and Geometry

该杂志探讨了几何和分析的全球问题，以及这些领域之间的相互作用及其在理论物理问题中的应用。它有助于扩大该领域研究成果的国际交流。ANNALS OF GLOBAL ANALYSIS AND GEOMETRY 涵盖的领域包括：全局分析、微分几何、复流形以及复分析和代数几何的相关结果、李群、李变换群和谐波分析、变分微积分、微分几何和全局分析在理论物理问题中的应用。

The Annals of Global Analysis and Geometry addresses global issues in the fields of geometry and analysis, as well as the interactions between these areas and their applications in theoretical physics. The journal aims to enhance international communication of research findings in this field. Topics covered include global analysis, differential geometry, complex manifolds and related results in complex analysis and algebraic geometry, Lie groups, Lie transformation groups, harmonic analysis, variational calculus, and the applications of differential geometry and global analysis in theoretical physics.

《Annals of Global Analysis and Geometry》探讨几何和分析领域的全球性问题，以及这些领域之间的相互作用及其在理论物理中的应用。该杂志旨在促进国际间在这一领域研究成果的交流。涵盖的主题包括全局分析、微分几何、复流形及其相关的复分析和代数几何结果、李群、李变换群、谐波分析、变分微积分，以及微分几何和全局分析在理论物理问题中的应用。

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数学	3
数学, 数学	3

Solution to the n-bubble problem on $$\mathbb {R}^1$$ with log-concave density

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