Published Paper
Inserted: 27 jul 2009
Last Updated: 30 jul 2020
Journal: J. Geom. Anal.
Volume: 20
Number: 2
Pages: 243-290
Year: 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.
Keywords: isoperimetric problem, Manifolds with density
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