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Full Description
The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner.
The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop—Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmüller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry.
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 current research trends in geometry.
Contents
1 Athanase Papadopoulos, Introduction.- 2 Marek Lassak, Spherical geometry - A survey on width and thickness of convex bodies.- 3 Vitor Balestro and Horst Martini, Minkowski geometry - some concepts and recent developments.- 4 Javier Alonso at al., Orthogonality types in normed linear spaces.- 5 Ivan Izmestiev, Mixed volumes and inequalities.- 6 Gérard Besson and Gilles Courtois, Compactness and finiteness results for Gromov-Hyperbolic spaces.- 7 Valentin Poénaru, All 4-dimensional smooth Schoenflies balls are geometrically simply-connected - A fast survey of the proof.- 8 Valentin Poénaru, Classical differential topology and non-commutative geometry.- 9 Daniel Massart, A short introduction to translation surfaces, Veech surfaces and Teichmüller dynamics.- 10 Ken'ichi Ohshika, Teichmüller spaces and the rigidity of mapping class action.- 11 Indranil Biswas and Sorin Dumitrescu, Holomorphic G-structures and foliated Cartan geometries on compact complex manifolds.
