Antonio Alarcón

collaborators

3 papers

math.DG2024

On the Gauss map assignment for minimal surfaces and the Osserman curvature estimate

Antonio Alarcon, Francisco J. Lopez

The Gauss map of a conformal minimal immersion of an open Riemann surface $M$ into $R^{n}$ , $n \geq 3$ , is a holomorphic map $M \to Q^{n - 2} \subset CP^{n - 1}$ . Deno…

math.DG2024

Generic properties of minimal surfaces

Antonio Alarcon, Francisco J. Lopez

Let $M$ be an open Riemann surface and $n \geq 3$ be an integer. In this paper we establish some generic properties (in Baire category sense) in the space of all conformal minimal im…

math.DG2024

The Mittag-Leffler theorem for proper minimal surfaces and directed meromorphic curves

Antonio Alarcon, Tjasa Vrhovnik

We establish a Mittag-Leffler-type theorem with approximation and interpolation for meromorphic curves $M \to C^{n}$ ( $n \geq 3$ ) directed by Oka cones in $C^{n}$ on an…