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.
Содержание
1 Athanase Papadopoulos: Introduction.- 2 Norbert A’Campo and Athanase Papadopoulos, Geometry of surfaces.- 3 Ken’ichi
Ohshika: Teichmuller spaces and their various metrics.- 4 Marc Troyanov: Double forms, curvature integrals and the Gauss-Bonnet formula.- 5 Graham Smith, Quaternions, Monge–Amp˜A¨re structures and κ-surfaces.- 6 Peter Kristel and Eric Schippers, Lagrangian Grassmannians of polarizations.- 7 Arpad Kurusa, Metric characterizations of projective-metric spaces.- 8 Arpad Kurusa, Supplement to “Metric Characterization of Projective-metric Spaces”.- 9 Boumediene Et-Taoui, Metric problems in projective and Grassmann spaces.- 10 Valeriı Berestovskiı and Yuriı Nikonorov, On the geometry of finite homogeneous subsets of Euclidean spaces.- 11 Gue-Seon Lee and Ludovic Marquis, Discrete Coxeter groups.- 12 Bruno Luiz Santos Correia and Marc Troyanov, Isoperimetry in Finitely Generated Groups.
Об авторе
Athanase Papadopoulos (born 1957) is Directeur de Recherche at the French Centre National de la Recherche Scientifique. His main fields of interest are geometry and topology, the history and philosophy of mathematics, and mathematics and music. He has held visiting positions at the Institute for Advanced Study, Princeton (1984–85 and 1993–94), USC (1998–1999), CUNY (Ada Peluso Professor, 2014), Brown University (Distinguished visiting professor, 2017), Tsinghua University, Beijing (2018), Lamé Chair of the State University of Saint Petersburg (2019), and has had several month visits to the Max-Plank Institute for mathematics (Bonn), the Erwin Schrödinger Institute (Vienna), the Graduate Center of CUNY (New York), the Tata Institute (Bombay), Galatasaray University (Istanbul), the University of Florence (Italy), Fudan University (Shanghai), Gakushuin University (Tokyo) and Presidency University (Calcutta). He is the author of more than 200 published articles and 35 monographsand edited books.
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