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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature


Authors: Frank Morgan, Michael Hutchings and Hugh Howards
Journal: Trans. Amer. Math. Soc. 352 (2000), 4889-4909
MSC (2000): Primary 53Cxx, 53Axx, 49Qxx
Published electronically: July 12, 2000
MathSciNet review: 1661278
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Abstract:

We prove that the least-perimeter way to enclose prescribed area in the plane with smooth, rotationally symmetric, complete metric of nonincreasing Gauss curvature consists of one or two circles, bounding a disc, the complement of a disc, or an annulus. We also provide a new isoperimetric inequality in general surfaces with boundary.


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Additional Information

Frank Morgan
Affiliation: Department of Mathematics, Williams College, Williamstown, Massachusetts 01267
Email: Frank.Morgan@williams.edu

Michael Hutchings
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Email: hutching@math.stanford.edu

Hugh Howards
Affiliation: Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109
Email: howards@wfu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02482-X
PII: S 0002-9947(00)02482-X
Keywords: Isoperimetric problem
Received by editor(s): July 10, 1998
Received by editor(s) in revised form: November 1, 1998
Published electronically: July 12, 2000
Article copyright: © Copyright 2000 American Mathematical Society