Displaying similar documents to “Existence results for embedded minimal surfaces of controlled topological type, II”

Complete minimal surfaces in R.

Francisco J. López, Francisco Martín (1999)

Publicacions Matemàtiques

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In this paper we review some topics on the theory of complete minimal surfaces in three dimensional Euclidean space.

Linearization and explicit solutions of the minimal surface equations.

Alexander G. Reznikov (1992)

Publicacions Matemàtiques

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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.