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THE ISOPERIMETRIC PROBLEM ON PLANES WITH DENSITY

Part of: Global differential geometry

Published online by Cambridge University Press:  01 October 2008

COLIN CARROLL ,
ADAM JACOB ,
CONOR QUINN  and
ROBIN WALTERS
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.

Keywords

isoperimetric problemplanes with densityGauss plane

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 177 - 197
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.

References

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