책 이미지
책 정보
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 미분기하학
· ISBN : 9783030866945
· 쪽수 : 467쪽
· 출판일 : 2022-02-19
책 소개
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, Teichmuller 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.
New feature
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, Teichmuller 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.
목차
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 Gerard Besson and Gilles Courtois, Compactness and finiteness results for Gromov-Hyperbolic spaces.- 7 Valentin Poenaru, All 4-dimensional smooth Schoenflies balls are geometrically simply-connected - A fast survey of the proof.- 8 Valentin Poenaru, Classical differential topology and non-commutative geometry.- 9 Daniel Massart, A short introduction to translation surfaces, Veech surfaces and Teichmuller dynamics.- 10 Ken'ichi Ohshika, Teichmuller 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.
