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The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature
Author(s):
Frank
Morgan;
Michael
Hutchings;
Hugh
Howards
Journal:
Trans. Amer. Math. Soc.
352
(2000),
4889-4909.
MSC (2000):
Primary 53Cxx, 53Axx, 49Qxx
Posted:
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:
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
Posted:
July 12, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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