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Displaying similar documents to “The isoperimetric inequality for a minimal surface with radially connected boundary”

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.