6 citations · 8 across the 4 of their papers we have counts for
6 papers · 1 filter
Complete minimal surfaces and harmonic functions
Antonio Alarcon, Isabel Fernandez, Francisco J. Lopez
We prove that for any open Riemann surface and any non constant harmonic function there exists a complete conformal minimal immersion $X:M \to \mathbb{R}^…
Complete minimal surfaces in R3 with a prescribed coordinate function
Antonio Alarcon, Isabel Fernandez
In this paper we construct complete simply connected minimal surfaces with a prescribed coordinate function. Moreover, we prove that these surfaces are dense in the space of all mi…
Compact complete proper minimal immersions in strictly convex bounded regular domains of R^3
Antonio Alarcon
Consider a strictly convex bounded regular domain of . For any arbitrary finite topological type we find a compact Riemann surface , an open domain $M\subset…
On the Calabi-Yau problem for maximal surfaces in L^3
Antonio Alarcon
In this paper we construct an example of a weakly complete maximal surface in the Lorentz-Minkowski space L^3, which is bounded by a hyperboloid. Moreover, all the singularities of…
Limit sets for complete minimal immersions
A. Alarcon, N. Nadirashvili
In this paper we study the behaviour of the limit set of complete proper compact minimal immersions in a regular domain G of R^3. We prove that the second fundamental form of the b…
A uniqueness theorem for the singly periodic genus-one helicoid
A. Alarcon, L. Ferrer, F. Martin
The singly periodic genus-one helicoid was in the origin of the discovery of the first example of a complete minimal surface with finite topology but infinite total curvature, the…