We prove that an isoperimetric region in R2 with density er must be convex and contain the origin, and provide numerical evidence that circles about the origin are isoperimetric, as predicted by the Log-Convex Density Conjecture.
Chung, Ping Ngai; Fernandez, Miguel A.; Shah, Niralle; and Vieira, Luis Sordo
"Are circles isoperimetric in the plane with density 𝑒ʳ?,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
1, Article 12.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss1/12