3 papers
math.DG2026
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…
math.CV2025
Oka-1 manifolds
Antonio Alarcon, Franc Forstneric
In this paper we begin a systematic study of the class of complex manifolds which are universal targets of holomorphic maps from open Riemann surfaces. We call them Oka-1 manifolds…
math.DG2024
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…