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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalization of the isoperimetric inequality on $ S\sp 2$ and flat tori in $ S\sp 3$


Author: Kazuyuki Enomoto
Journal: Proc. Amer. Math. Soc. 120 (1994), 553-558
MSC: Primary 53A04; Secondary 53C42
MathSciNet review: 1163333
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Abstract: A geometric inequality is proved for closed curves on $ {S^2}$ which are regularly homotopic to simple closed curves. This generalizes the classical isoperimetric inequality for simple closed curves on $ {S^2}$. The proof is based on the study of flat tori in $ {S^3}$ and their images under the Gauss map.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1163333-7
PII: S 0002-9939(1994)1163333-7
Keywords: Isoperimetric inequality, flat torus, Gauss map
Article copyright: © Copyright 1994 American Mathematical Society