Calculus of Variations and Geometric Measure Theory

A. CaƱete - Michele Miranda Jr. - D. Vittone

Some isoperimetric problems in planes with density

created by vittone on 27 Jul 2009
modified on 30 Jul 2020


Published Paper

Inserted: 27 jul 2009
Last Updated: 30 jul 2020

Journal: J. Geom. Anal.
Volume: 20
Number: 2
Pages: 243-290
Year: 2010

ArXiv: 0906.1256 PDF


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