Are circles isoperimetric in the plane with density 𝑒ʳ?

Authors

Ping Ngai Chung, University of Cambridge
Miguel A. Fernandez, Truman State University
Niralle Shah, Willams College
Luis Sordo Vieira, University of Kentucky

Abstract

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.

Author Bio

Ping Ngai Chung recently graduated from MIT and is an incoming masters student at the University of Cambridge. He will be a graduate student at the University of Chicago starting Fall 2015.Faculty Sponsor: Frank Morgan, Atwell Professor of Mathematics, Williams College

Miguel Fernandez is a graduate student at Penn State University and currently works for the LIGO Collaboration. He is a graduate of Truman State University.

Niralee K. Shah, a graduate of Williams College, is a previous mathematics teacher at King's Academy in Jordan and now works at a tech startup in Palestine.

Luis Sordo Vieira is a graduate student at the University of Kentucky and a recipient of the National Science Foundation graduate research fellowship award. He is a graduate of Wayne State University.

Faculty Sponsor

Frank Morgan

Recommended Citation

Chung, Ping Ngai; Fernandez, Miguel A.; Shah, Niralle; and Vieira, Luis Sordo (2015) "Are circles isoperimetric in the plane with density 𝑒ʳ?," Rose-Hulman Undergraduate Mathematics Journal: Vol. 16: Iss. 1, Article 12.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss1/12