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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 | References | Similar Articles | Additional Information


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

Michael Hutchings
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305

Hugh Howards
Affiliation: Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109

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