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Isoperimetric curves on hyperbolic surfaces


Authors: Colin Adams and Frank Morgan
Journal: Proc. Amer. Math. Soc. 127 (1999), 1347-1356
MSC (1991): Primary 30F99, 53C99, 53A99, 49Q99
Published electronically: January 28, 1999
MathSciNet review: 1487351
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Abstract | References | Similar Articles | Additional Information

Abstract: Least-perimeter enclosures of prescribed area on hyperbolic surfaces are characterized.


References [Enhancements On Off] (What's this?)

  • [A] Colin Adams, Maximal cusps, collars and systoles for hyperbolic surfaces, Indiana Univ. Math. J., to appear.
  • [HM] Joel Hass and Frank Morgan, Geodesics and soap bubbles in surfaces, Math. Z. 223 (1996), no. 2, 185–196. MR 1417428, 10.1007/PL00004560
  • [HHM] Hugh Howards, Michael Hutchings, and Frank Morgan, The isoperimetric problem on surfaces, Amer. Math. Monthly, to appear.
  • [M] Frank Morgan, Geometric measure theory, 2nd ed., Academic Press, Inc., San Diego, CA, 1995. A beginner’s guide. MR 1326605
  • [S] P. Schmutz, Riemann surfaces with shortest geodesic of maximal length, Geom. Funct. Anal. 3 (1993), no. 6, 564–631. MR 1250756, 10.1007/BF01896258

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Additional Information

Colin Adams
Affiliation: Department of Mathematics, Williams College, Williamstown, Massachusetts 01267
Email: colin.adams@williams.edu

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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04778-4
Keywords: Isoperimetric problem, hyperbolic surface
Received by editor(s): August 6, 1997
Published electronically: January 28, 1999
Communicated by: Christopher B. Croke
Article copyright: © Copyright 1999 American Mathematical Society