We study the isoperimetric problem in the plane with weighting or density e-1/r. The isoperimetric problem seeks to enclose prescribed weighted area with minimum weighted perimeter. For density e-1/r, isoperimetric curves are conjectured to pass through the origin. We provide numerical and theoretical evidence that such curves have an angle at the origin approaching 1 radian from above as area approaches zero and provide further estimates.
Dr. Frank Morgan, Department of Mathematics and Statistics, Williams College
Gallagher, Paul; Hu, David; Martin, Zane; Miller, Maggie; and Perpetua, Byron
"Isoperimetry in the Plane with Density e-1/r,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss2/7