A Note on Stability of Minimal Surfaces in n-dimensional Hyperbolic Space Hn(c)

Li Haizhong

Displaying similar documents to “A Note on Stability of Minimal Surfaces in n-dimensional Hyperbolic Space Hn(c)”

A note on stability of minimal surfaces in $n$ -dimensional hyperbolic space $H^{n} (c)$ .

Li, Haizhong (1997)

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Linearization and explicit solutions of the minimal surface equations.

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We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation Δh + 2h = 0 describing locally germs of minimal surfaces. Here Δ is the Laplace-Beltrami operator on the standard two-dimensional sphere. It explains the existence of the sum operator of minimal surfaces, introduced recently. In 4-dimensional space the equation Δ h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.