Abstract
In this paper, we will consider a family $\mathscr{Y}$ of complete CAT(0) spaces such that the tangent cone TCp Y at each point p $\in$ Y of each Y $\in$ $\mathscr{Y}$ is isometric to a (finite or infinite) product of the Euclidean cones Cone(Xα) over elements Xα of some Gromov-Hausdorff precompact family {Xα} of CAT(1) spaces. Each element of such $\mathscr{Y}$ is a space presented by Gromov [4] as an example of a "CAT(0) space with "bounded" singularities". We will show that the Izeki-Nayatani invariants of spaces in such a family are uniformly bounded from above by a constant strictly less than 1.
Citation
Tetsu Toyoda. "CAT(0) spaces on which a certain type of singularity is bounded." Kodai Math. J. 33 (3) 398 - 415, October 2010. https://doi.org/10.2996/kmj/1288962550
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