Some isoperimetric problems in planes with density

Details Some isoperimetric problems in planes with density Some isoperimetric problems in planes with density

2009-06-08

arxiv.org/abs/0906.1256v1

Mathematics

Differential Geometry

40 pages, 19 figures

Scientific paper

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 $\R^2$. Finally, we
give a list of related open questions.

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