43 citations · 356 across the 52 of their papers we have counts for
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Complete non-orientable minimal surfaces of finite total curvature: Approximation and interpolation
Antonio Alarcon, Francisco J. Lopez
In this paper, we prove a uniform approximation theorem with interpolation for complete non-orientable minimal surfaces of finite total curvature in the Euclidean space $\mathbb{R}…
Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure
Antonio Alarcon, Ildefonso Castro-Infantes, Jorge Hidalgo
We prove that every open Riemann surface is the complex structure of a complete surface of constant mean curvature 1 (CMC-1) in the 3-dimensional hyperbolic space $\mathbb{H}^3…
Proper harmonic embeddings of open Riemann surfaces into
Antonio Alarcon, Francisco J. Lopez
We prove that every open Riemann surface admits a proper embedding into by harmonic functions. This reduces by one the previously known embedding dimension in this f…
The space of Gauss maps of complete minimal surfaces
Antonio Alarcon, Finnur Larusson
The Gauss map of a conformal minimal immersion of an open Riemann surface into is a meromorphic function on . In this paper, we prove that the Gauss map assign…
A strong parametric h-principle for complete minimal surfaces
Antonio Alarcon, Finnur Larusson
We prove a parametric h-principle for complete nonflat conformal minimal immersions of an open Riemann surface into , . It follows that the inclusion of t…
Erratum to "Interpolation and optimal hitting for complete minimal surfaces with finite total curvature"
Antonio Alarcon, Ildefonso Castro-Infantes, Francisco J. Lopez
We correct a mistake in the paper with the mentioned title and reference: Calc. Var. Partial Differential Equations 58 (2019), no. 1, 58:21. It corresponds with the preprint arXiv:…