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

Linearization and explicit solutions of the minimal surface equations.

Alexander G. Reznikov (1992)

Publicacions Matemàtiques

Similarity:

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.

On Veronese-Borůvka spheres

Katsuei Kenmotsu (1997)

Archivum Mathematicum

Similarity:

In this paper, history of reserches for minimal immersions from constant Gaussian curvature 2-manifolds into space forms is explained with special emphasis of works of O. Borůvka. Then recent results for the corresponding probrem to classify minimal immersions of such surfaces in complex space forms are discussed.