The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature
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- by Frank Morgan, Michael Hutchings and Hugh Howards
- Trans. Amer. Math. Soc. 352 (2000), 4889-4909
- DOI: https://doi.org/10.1090/S0002-9947-00-02482-X
- Published electronically: July 12, 2000
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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.References
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Bibliographic 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
- Received by editor(s): July 10, 1998
- Received by editor(s) in revised form: November 1, 1998
- Published electronically: July 12, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 4889-4909
- MSC (2000): Primary 53Cxx, 53Axx, 49Qxx
- DOI: https://doi.org/10.1090/S0002-9947-00-02482-X
- MathSciNet review: 1661278