Calculus of Variations and Geometric Measure Theory

G. He - P. Zhao

The isoperimetric problemin the Heisenberg group $H^n$ with density

created by zhao on 27 Jul 2020


Published Paper

Inserted: 27 jul 2020

Journal: Analysis and Mathematical Physics
Pages: 23
Year: 2020
Doi: 10.1007/s13324-020-00367-2


We study the isoperimetric problem for the axially symmetric sets in the Heisenberg group $H^n$ with density $
^p$. At first, we prove the existence of weighted isoperimetric sets.Then,we characterize weighted isoperimetric sets uniquely as bubble sets. Finally, we deduce an interesting result that, up to a constant multiplicator, $
^p$ is the only horizontal radial density for which bubble sets can be weighted isoperimetric sets.