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THE ISOPERIMETRIC PROBLEM ON PLANES WITH DENSITY

Published online by Cambridge University Press:  01 October 2008

COLIN CARROLL
Affiliation:
Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA (email: [email protected])
ADAM JACOB
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA (email: [email protected])
CONOR QUINN
Affiliation:
Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA (email: [email protected])
ROBIN WALTERS*
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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We discuss the isoperimetric problem in planes with density. In particular, we examine planes with generalized curvature zero. We solve the isoperimetric problem on the plane with density ex, as well as on the plane with density rp for p<0. The Appendix provides a proof by Robert Bryant that the Gauss plane has a unique closed geodesic.

Type
Research Article
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

Our thanks are due to the National Science Foundation for grants to Morgan and SMALL, and Williams College.

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