Inserted: 27 jul 2009
Last Updated: 30 jul 2020
Journal: J. Geom. Anal.
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.
Keywords: isoperimetric problem, Manifolds with density