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Results tagged with alexandrov-geometry
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Alexandrov geometry studies non smooth analogues of Riemannian manifolds with curvature bounded from below or above. It includes spaces with curvature bounded below (briefly $\mathrm{CBB}[\kappa]$) and spaces with curvature bounded above (briefly $\mathrm{CAT}[\kappa]$).
8
votes
infinite dimensional CAT(0) groups
First, I suppose that by proper action you mean the one in the sense of Bridson and Haefliger, otherwise you would have to regard ${\mathbb R}$ as a $CAT(0)$ groups. Now, it follows from Eric Swenson' …
- 31.2k
4
votes
Does every CAT(0) space embed in a measurable integral of $\mathbb{R}$-trees?
Here is an answer to the 1st question using group theory. Any NPC symmetric space whose isometrically group has property T does not embed isometrically into a product of real trees. The reason is that …
- 31.2k
1
vote
when are local quasigeodesics global in CAT(0)
Local-to-global results for "Morse quasigeodesics" in symmetric spaces are proven in section 7 of this paper that I wrote with Bernhard Leeb and Joan Porti.
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