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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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