As a special case, a complete CAT(0) space is also known as a Hadamard space; this is by analogy with the situation for Hadamard manifolds.

2024年6月14日 · In Chapters 1 and 2 we first discuss how to define the length of curves, and geodesics on (X,d), and then using these to portray the notion of ``non-positive curvature'' for …

M ̈unster, June 22, 2004 “CAT(0)-space” is a term invented by Gromov. Also, called “Hadamard space.” Roughly, a space which is “non- positively curved” and simply connected. Theorem. …

2014年1月1日 · Complete CAT (0) spaces are often called Hadamard spaces. CAT (0) spaces have a remarkably nice geometric structure. One can see almost immediately that in such …

First self-contained, comprehensive introduction to CAT(0) cube complexes; Topics range from basic prerequisites to a variety of advanced topics; Suitable for use in a graduate course or for …

2024年1月13日 · A 0 0-category (or (0, 0) (0,0)-category) is, up to equivalence, the same as a set (or class).

A CAT(0) space is a geodesic metric space all of whose triple of points ( x,y,z ) ∈ X 3 satisfy the following condition: given a Euclidean comparison triangle (ˆ x,y, ˆ ˆz) in R 2 , any point p ∈ X …

I have a question regarding the definition of CAT(0) spaces. I am using the following definition: $X$ complete metric space is CAT(0) if $\forall z,y \in X$, $\exists m \in X$ such that $\forall x...

2015年2月4日 · Cat(0) spaces have unique geodesics between points. Fix a base point, and along each geodesic out from that point, pull everything inwards. This is well-defined because …

We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension d for all d ≥ 4 (see Theorem 2.13). These examples result from applying CAT(0)/CAT(−1) …