Stable complete constant mean curvature surfaces in 𝑅³ and 𝐻³

Mori, Hiroshi

doi:10.1090/S0002-9947-1983-0701517-7

Stable complete constant mean curvature surfaces in $\textbf {R}^{3}$ and $H^{3}$
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Trans. Amer. Math. Soc. 278 (1983), 671-687 Request permission

Abstract:

We construct some $1$-parameter families of complete rotation surfaces with constant mean curvature in the hyperbolic $3$-space ${H^3}$ of constant sectional curvature $-1$, and show that some of them are stable for the variational problem of area together with oriented volume, and that a complete connected, oriented surface with constant mean curvature in the Euclidean $3$-space ${R^3}$ which is stable for the variational problem is a plane.

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