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.
Some Isoperimetric Problems in Planes with Density
VITTONE, DAVIDE
2010
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 R^2. Finally, we give a list of related open questions.
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