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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Total curvatures and minimal areas of complete surfaces


Author: Katsuhiro Shiohama
Journal: Proc. Amer. Math. Soc. 94 (1985), 310-316
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1985-0784184-3
MathSciNet review: 784184
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Abstract: Minimal areas for certain classes of finitely connected complete open surfaces are obtained by using a Bonnesen-style isoperimetric inequality for large balls on the surfaces. In particular, the minimal area of Riemannian planes whose Gaussian curvatures are bounded above by 1 is $ 4\pi $.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0784184-3
Keywords: Complete manifolds, Gaussian curvature, geodesics, isoperimetric inequality
Article copyright: © Copyright 1985 American Mathematical Society