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

 

Minimal surfaces and $ H$-surfaces in non-positively curved space forms


Author: Bennett Palmer
Journal: Proc. Amer. Math. Soc. 119 (1993), 245-250
MSC: Primary 53C42; Secondary 53A10, 58E12
MathSciNet review: 1180466
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Abstract: We show that if the Gauss curvature of a surface of constant mean curvature in a nonpositively curved space form is sufficiently pinched, the surface is stable. In this case, we also give an upper bound for the inradius. We then show that the inradius of a stable minimal surface in Euclidean space, which is contained in a solid cylinder, is bounded above by a constant depending only on the radius of the cylinder.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1180466-9
PII: S 0002-9939(1993)1180466-9
Article copyright: © Copyright 1993 American Mathematical Society