New York Journal of Mathematics
Volume 16 (2010) 31-51

Volume 16

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Jonathan Dahlberg, Alexander Dubbs, Edward Newkirk, and Hung Tran

Isoperimetric regions in the plane with density rp

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Published: May 5, 2010
Keywords: Isoperimetric, plane with density, radial densities, symmetrization
Subject: 53A10, 49Q20
Abstract
We consider the isoperimetric problem in the plane with density rp, p > 0, and prove that the solution is a circle through the origin. We use the stability of this isoperimetric curve to prove an apparently new generalization of Wirtinger's Inequality.
Acknowledgements

This paper represents work of the 2008 SMALL research Geometry Group. We would like to thank Williams College and the National Science Foundation REU for funding SMALL
Author information

Jonathan Dahlberg:
Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267
09jrd@williams.edu

Alexander Dubbs:
Department of Mathematics, Harvard University, Cambridge, MA 02138
alex.dubbs@gmail.com

Edward Newkirk:
Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267
09esn@williams.edu

Hung Tran:
Department of Mathematics, Berea College, Berea, KY 40404
hungttrancd@gmail.com

Queries about the paper:
Frank Morgan, Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267
Frank.Morgan@williams.edu