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...

In a region where the curvature of the surface satisfies K ≤ 0, geodesic triangles satisfy the CAT(0) inequalities of comparison geometry, studied by Cartan, Alexandrov and Toponogov, and considered later from a different point of view by Bruhat and Tits.

“CAT(0)-space” is a term invented by Gromov. Also, called “Hadamard space.” Roughly, a space which is “non-positively curved” and simply connected. C = “Comparison” or “Cartan” A = “Aleksandrov” T = “Toponogov”

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 which belongs to some geodesic

2018年3月15日 · This paper presents a consensus algorithm of dynamical points in a CAT(0) space, and demonstrates its application to the distributed fusion problem of phylogenetic trees, together with a study on its robustness and efficiency. All the work is helpful for the fusion of tree-type data in practice and the motion control in a nonlinear space.

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 independent study

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 spaces angles exist in a strong sense, the distance function is convex, one has both uniform convexity and orthogonal projection onto convex subsets, etc.

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 spaces angles exist in a strong sense, the distance function is convex, one has both uniform convexity and orthogonal projection onto convex subsets, etc.

A CAT(0) space is a uniquely geodesic space such that for every triple of dis-tinct points x,y,z∈ X, the geodesic triangle is no fatter than the corresponding comparison triangle in Euclidean R2 (the triangle with the same edge lengths). A detailed account of CAT(0) spaces is found in [1] or [2].

2023年1月29日 · post传：action=||&data='cat /flag' 0o0 这里没有发现什么有用的东西，我们去扫一扫目录看看，然后我们就发现了，一个关键的文件，.D