In the name of of Allah the Merciful

Surveys in Geometry I

Athanase Papadopoulos, 978-3-030-86695-2, 978-3-030-86694-5, 3030866947, 978-3030866945, 9783030866945, B09SW9F49G

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English | 2022 | PDF

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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.