Some isoperimetric problems in planes with density

2009/06/08 by Antonio Cañete, Cañete, Antonio, Michele Miranda +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.0906.1256

openalex publication_date 2009/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteristic functions of half-planes, strips and balls. We also consider continuous modification of Gauss density in \R². Finally, we give a list of related open questions.

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