New Trends in Geometric Analysis (eBook)

The aim of this book is to provide an overview of some of the progress made by the Spanish Network of Geometric Analysis (REAG, by its Spanish acronym) since its born in 2007. REAG was created with the objective of enabling the interchange of ideas and the knowledge transfer between several Spanish groups having Geometric Analysis as a common research line. This includes nine groups at Universidad Autónoma de Barcelona, Universidad Autónoma de Madrid, Universidad de Granada, Universidad Jaume I de Castellón, Universidad de Murcia, Universidad de Santiago de Compostela and Universidad de Valencia. The success of REAG has been substantiated with regular meetings and the publication of research papers obtained in collaboration between the members of different nodes.

Antonio Alarcón is a Professor at the Department of Geometry and Topology in the University of Granada. His research interests are included in the field of Geometric Analysis, lying 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. 

Vicente Palmer is a Professor of Geometry in the Department of Mathematics of Universitat Jaume I in Castellón, (Spain). He teaches mathematics in different degrees of the university and his research focuses in the study of potential analysis in Riemannian manifolds from the viewpoint of submanifold theory, and their connections with the Dirichlet spectrum of Riemannian manifolds and the exit time moments of Brownian motion defined on them. In addition to these abstruse and obscure subjects, he has devoted part of his work to the slightly more mundane (apparently simpler but definitely no less shady) problems of university management, holding the post of vice-rector for economic affairs at Jaume I University for 5 years.

César Rosales is an Associate Professor at the Department of Geometry and Topology in the University of Granada. His research focuses on geometric optimization problems, mainly those related to the area functional. He has studied isoperimetric problems and minimal surfaces in metric-measure spaces by means of mathematical techniques like calculus of variations, geometric measure theory and partial differential equations. His main contributions include classification results for isoperimetric and constant mean curvature surfaces in some relevant settings, like the sub-Riemannian Heisenberg group or the Gaussian space.