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The book is the second volume of a collection which consists of surveys that focus on important topics in geometry which are at the heart of current research. The topics in the present volume include the conformal and the metric geometry of surfaces, Teichmüller spaces, immersed surfaces of prescribed extrinsic curvature in 3-dimensional manifolds, symplectic geometry, the metric theory of Grassmann spaces, homogeneous metric spaces, polytopes, the higher-dimensional Gauss–Bonnet formula, isoperimetry in finitely generated groups and Coxeter groups.
Each chapter is intended for graduate students and researchers. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to important topics in geometry.
Preface
Editor and Contributors
About the Editor
Contributors
Introduction
Geometry on Surfaces, a Source for Mathematical Developments
Teichmüller Spaces and Their Various Metrics
Double Forms, Curvature Integrals and the Gauss–Bonnet Formula
Appendix A: Some Background in Differential Geometry
Quaternions, Monge–Ampère Structures and k-Surfaces
Lagrangian Grassmannians of Polarizations
Metric Characterizations of Projective-Metric Spaces
Supplement to ``Metric Characterization of Projective-Metric Spaces''
Metric Problems in Projective and Grassmann Spaces
On the Geometry of Finite Homogeneous Subsets of Euclidean Spaces
Discrete Coxeter Groups
Isoperimetry in Finitely Generated Groups
Index