New Trends in Geometric Analysis

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 theDirichlet 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.

• - Snapshots of Non-local Constrained Mean Curvature-Type Flows. - Spherical Curves Whose Curvature Depends on Distance to a Great Circle. - Conjugate Plateau Constructions in Product Spaces. - Integral Geometry of Pairs of Lines and Planes. - Homogeneous Hypersurfaces in Symmetric Spaces. - First Dirichlet Eigenvalue and Exit Time Moments: A Survey. - Area-Minimizing Horizontal Graphs with Low Regularityin the Sub-Finsler Heisenberg Group H1. - On the Double Soul Conjecture. - Consequences and Extensions of the Brunn-Minkowski Theorem. - An Account on Links Between Finsler and Lorentz Geometries for Riemannian Geometers. - Geometric and Architectural Aspects of the Singular Minimal Surface Equation. - Geometry of [ɸ, e3]-Minimal Surfaces in R3. - Uniqueness of Constant Mean Curvature Spheres.