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Cauchy problems for discrete affine minimal surfaces

Marcos Craizer, Thomas Lewiner, Ralph Teixeira (2012)

Archivum Mathematicum

In this paper we discuss planar quadrilateral (PQ) nets as discrete models for convex affine surfaces. As a main result, we prove a necessary and sufficient condition for a PQ net to admit a Lelieuvre co-normal vector field. Particular attention is given to the class of surfaces with discrete harmonic co-normals, which we call discrete affine minimal surfaces, and the subclass of surfaces with co-planar discrete harmonic co-normals, which we call discrete improper affine spheres. Within this classes,...

Complete minimal surfaces in 3 with type Enneper end

Nedir Do Espirito Santo (1994)

Annales de l'institut Fourier

We show that there exists a complete minimal surface immersed into 3 which is conformally equivalent to a compact hyperelliptic Riemann surface of genus three minus one point. The end of the surface is of Enneper type and its total curvature is - 16 π .

Complete minimal surfaces in R3.

Francisco J. López, Francisco Martín (1999)

Publicacions Matemàtiques

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

Complete minimal surfaces of arbitrary genus in a slab of 3

Celso J. Costa, Plinio A. Q. Simöes (1996)

Annales de l'institut Fourier

In this paper we construct complete minimal surfaces of arbitrary genus in 3 with one, two, three and four ends respectively. Furthermore the surfaces lie between two parallel planes of 3 .

Concentrated monotone measures with non-unique tangential behavior in 3

Robert Černý, Jan Kolář, Mirko Rokyta (2011)

Czechoslovak Mathematical Journal

We show that for every ε > 0 there is a set A 3 such that 1 A is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and 1 A has the 1 -dimensional density between 1 and 2 + ε everywhere in the support.

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