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

Palmer, Bennett

doi:10.1090/S0002-9939-1993-1180466-9

Minimal surfaces and $H$-surfaces in non-positively curved space forms
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Proc. Amer. Math. Soc. 119 (1993), 245-250 Request permission

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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