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Jonathan Dahlberg, Alexander Dubbs, Edward Newkirk, and Hung Tran
Isoperimetric regions in the plane with density rp view print
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| Published: |
May 5, 2010 |
| Keywords: |
Isoperimetric, plane with density, radial densities, symmetrization |
| Subject: |
53A10, 49Q20 |
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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.
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| 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
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| 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
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