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The isoperimetric problem on some singular surfaces

Abstract

We characterize least-perimeter enclosures of prescribed area on some piecewise smooth manifolds, including certain polyhedra, double spherical caps, and cylindrical cans.

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References
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[1]Almgren, F., ‘Spherical symmetrization’, in: Proceedings of the International Workshop on Integral Functionals in Calculus of Variations, (Trieste, 1985) Suppl. Rend. Circ. Mat. Palermo (2) 15 (1987) pp. 1125.
[2]Barber, M., Tice, J. and Wecht, B., ‘Geodesics and geodesic nets on regular polyhedra’, Williams College NSF ‘SMALL’ undergraduate research Geomtry Group report(1995).
[3]Bray, H. and Morgan, F., ‘An isoperimetric comparison theorem for Schwarzschild space and other manifolds’, Proc. Amer. Math. Soc. 130 (2002), 14671472.
[4]Burago, Yu. D. and Zalgaller, V. A., Geometric inequalities (Springer, New York, 1980).
[5]Erchak, A., Melinck, T. and Nicholson, R., ‘Geodesic nets on regular polyhedra’, Williams College NSF ‘SMALL’, undergraduate research Geometry Group report (1996).
[6]Federer, H., Geometric measure theory (Springer, New York, 1969).
[7]Gnepp, A., Ng, T. and Yoder, C., ‘Isoperimetric domains on polyhedra and singular surfaces’, Williams College NSF ‘SMALL’ undergraduate research Geometry Group report (1998).
[8]Heppes, A., e-mail communication to M. Barber, J. Tice, B. Wecht and F. Morgan, 1995.
[9]Howards, H., Hutchings, M. and Morgan, F., ‘The isoperimetric problem on surfaces’, Amer. Math. Monthly 106 (1999), 430439.
[10]Ivanov, A. O. and Tuzhilin, A. A., Minimal networks: the Steiner problem, and its generalizations (CRC Press, Boca Raton, 1994).
[11]Morgan, F., ‘An isoperimetric inequality for the thread problem’, Bull. Austral. Math. Soc. 55 (1997), 489495.
[12]Morgan, F., Geometric measure theory: a beginner's guide, 3rd edition (Academic Press, San Diego, 2000).
[13]Morgan, F., ‘Area-minimizing surfaces in cones’, Comm. Anal. Geom. 10 (2002), 971983.
[14]Morgan, F., ‘Regularity of isoperimetric hypersurfaces in Riemannian manifolds’, Trans. Amer. Math. Soc. 355 (2003), 50415052.
[15]Morgan, F., ‘In polytopes, small balls about some vertex minimize perimeter’, J. Differential Geom., to appear.
[16]Morgan, F. and Ritoré, M., ‘Isoperimetric regions in cones’, Trans. Amer. Math. Soc. 354 (2002), 23272339.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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