Displaying similar documents to “Complete minimal surfaces of arbitrary genus in a slab of ℝ 3 ”

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.

Applications of Quaternionic Holomorphic Geometry to minimal surfaces

K. Leschke, K. Moriya (2016)

Complex Manifolds

Similarity:

In this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the...