New Trends in Geometric Analysis

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.
On the occasion of the 15th anniversary of REAG this book aims to collect some old and new contributions of this network to Geometric Analysis. The book consists of thirteen independent chapters, all of themauthored by current members of REAG. The topics under study cover geometric flows, constant mean curvature surfaces in Riemannian and sub-Riemannian spaces, integral geometry, potential theory and Riemannian geometry, among others. Some of these chapters have been written in collaboration between members of different nodes of the network, and show the fruitfulness of the common research atmosphere provided by REAG. The rest of the chapters survey a research line or present recent progresses within a group of those forming REAG.
Surveying several research lines and offering new directions in the field, the volume is addressed to researchers (including postdocs and PhD students) in Geometric Analysis in the large.

Covers different topics and applications in geometric analysis Gathers scientific contributions of the Spanish Network of Geometric Analysis in the last 15 years Includes original research and comprenhensive surveys on related problems within geometric analysis

Autorentext

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.

Inhalt

• 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 [, e3]-Minimal Surfaces in R3. - Uniqueness of Constant Mean Curvature Spheres.