Antonio Alarcón
Antonio Alarcón
Catedrático de Universidad / Full Professor Universidad de Granada

Antonio Alarcón

Departamento de Geometría y Topología • Instituto de Matemáticas (IMAG)
Universidad de Granada

Research Interests

My research is included in the field of Geometric Analysis; my interests lie primarily in minimal surfaces, Riemann surfaces, complex geometry, and holomorphic contact geometry.

Most of my main results contribute to the study of minimal surfaces in the Euclidean space $\mathbb{R}^n$ by using Complex Analytic tools; in particular, the classical theory of approximation and interpolation for holomorphic mappings and the modern Oka theory. That is the subject of our book with Franc Forstnerič and Francisco J. López entitled Minimal Surfaces from a Complex Analytic Viewpoint, Springer Monographs in Mathematics (2021), Springer International Publishing.

In the last few years I have also studied other topics, such as constant mean curvature one surfaces in the hyperbolic space $\mathbb{H}^3$ (also called Bryant surfaces), complex curves in $\mathbb{C}^2$, and more generally complex hypersurfaces in the complex Euclidean space $\mathbb{C}^n$, holomorphic null curves in $\mathbb{C}^n$ and in the special linear group $\text{SL}_2(\mathbb{C})$, and holomorphic Legendrian curves in complex contact manifolds.

Minimal Surfaces from a Complex Analytic Viewpoint

Springer Monographs in Mathematics

(2021)

Research Grants

Together with Joaquín Pérez, we coordinate the research project Geometric Analysis (PID2023-150727NB-I00).

I am currently engaged in the following research grants:

Organization of Events