A Course in Metric GeometryAmerican Mathematical Soc., 2001 - 415 ページ "Metric geometry" is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). |
目次
Length Spaces | 25 |
Constructions | 59 |
Spaces of Bounded Curvature | 101 |
1 | 111 |
Smooth Length Structures | 135 |
Curvature of Riemannian Metrics | 209 |
7 | 241 |
Largescale Geometry | 271 |
9 | 307 |
10 | 351 |
13 | 375 |
17 | 387 |
| 405 | |
| 406 | |
| 412 | |
他の版 - すべて表示
多く使われている語句
Alexandrov space asymptotic cone bi-Lipschitz boundary Br(p circle comparison triangle connected consider constant convergence convex set coordinate system coordinate vector Corollary corresponding curvature bounded defined definition denote differential dimension disc distance function endpoints equal equivalent Euclidean plane example Exercise exists expp finite formula Gaussian curvature geodesic geometry gluing Gromov hyperbolic Hadamard space Hausdorff Hausdorff distance hence homeomorphic hyperbolic plane implies intrinsic metric isometry k-plane Lemma length space length structure lines Lipschitz locally compact map f metric space n-dimensional neighborhood nonnegative curvature nonnegatively curved nonpositive curvature norm orthogonal parameterized Poincaré model Proof properties Proposition prove radius resp Riemannian manifold Riemannian metric segment sequence shortest path smooth space of curvature space of directions space of nonpositive sphere subset surface tangent cone Theorem topological triangle abc triangle inequality two-dimensional unique vector fields word metric