The research interests of Antonio Alarcón lie primarily in minimal surfaces, Riemann surfaces, complex geometry, and holomorphic contact geometry. His main results contribute to the study of the global theory of minimal surfaces in Euclidean spaces by using both classical and modern complex analytic methods. He also studied Bryant surfaces in the hyperbolic space, complex curves and hypersurfaces in complex Euclidean spaces, and holomorphic Legendrian curves in complex contact manifolds.

Franc Forstneri¿ is a complex analyst who has made major contributions to the Cauchy-Riemann geometry, the theory and applications of holomorphic automorphisms of complex Euclidean spaces and related complex manifolds with large automorphism groups, and modern Oka theory, focusing on solving nonlinear complex analytic problems in the absence of topological obstructions. In the last decade he has been applying complex analytic methods to minimal surfaces and holomorphic contact geometry.

Francisco J. López is a specialist in the global theory of minimal surfaces in complete flat manifolds, Riemann surfaces, and complex analysis. Among his main contributions are those concerning the Gauss map of minimal surfaces, the geometry of complete minimal surfaces of finite total curvature, the Calabi-Yau problem, approximation and interpolation theory, and global geometry of complex curves.

The first book treating minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed only recently

Treats the global theory of minimal surfaces with a given complex structure, providing new results

Offers new directions in the theory of minimal surfaces and exposes several challenging open problems