Displaying similar documents to “Minimal surfaces of finite type”

Complete minimal surfaces in R.

Francisco J. López, Francisco Martín (1999)

Publicacions Matemàtiques

Similarity:

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

A rigidity theorem for Riemann's minimal surfaces

Pascal Romon (1993)

Annales de l'institut Fourier

Similarity:

We describe first the analytic structure of Riemann’s examples of singly-periodic minimal surfaces; we also characterize them as extensions of minimal annuli bounded by parallel straight lines between parallel planes. We then prove their uniqueness as solutions of the perturbed problem of a punctured annulus, and we present standard methods for determining finite total curvature periodic minimal surfaces and solving the period problems.

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.