Minimal surfaces and -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:
https://doi.org/10.1090/S0002-9939-1993-1180466-9

Article copyright:
© Copyright 1993
American Mathematical Society