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Results tagged with non-positive-curvature
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user 5010
11
votes
1
answer
492
views
Is the center of gravity in a CAT(0) space contained in the convex hull?
In reading Greg Kuperberg's partial answer to this question Convex hull in CAT(0) ,
I started wondering if the center of gravity is always contained in the closed convex hull.
More precisely, given $ …
- 10.1k
12
votes
1
answer
325
views
What are the extremal CAT(0) metrics?
(Split off from Does every CAT(0) space embed in a measurable integral of $\mathbb{R}$-trees? )
Fix an integer $k \ge 2$, and let
$MC0_k \subset \mathbb{R}^{\binom{k}{2}}$ be the set of possible squa …
- 10.1k
14
votes
3
answers
750
views
Does every CAT(0) space embed in a measurable integral of $\mathbb{R}$-trees?
Question 1. Does every CAT(0) space embed isometrically inside an integral of $\mathbb{R}$-trees?
Here an integral of $\mathbb{R}$ trees means the set of functions from a measure space $\mathcal{F}$ t …
- 10.1k