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4
votes
0answers
100 views

Fourier analysis for the discrete cube in CAT(0) spaces?

Is there a meaningful Fourier analysis of mappings from the discrete cube into CAT(0) spaces? Examples for what I have in mind: Fix a CAT(0) space $X$, a mapping $f:\{-1,1\}^n \to X$, and ...
12
votes
3answers
329 views

Embedding expanders in CAT(0) spaces

It is well-known that expanders are hard to embed into Hilbert (or $\ell^p$) spaces - any embedding of an expander with $n$ vertices has distortion $\Omega(\log n)$. Can anyone provide a reference ...
6
votes
0answers
210 views

Negative curvature in the middle of $R^{3}$

What's a simple example of metric on $R^{3}$ which has negative scalar curvature inside of a (limited) set N, and is equal to the standard (Euclidean) metric outside? Basically, I am asking for a ...
2
votes
1answer
246 views

Volume of a geodesic simplex on a manifold of non-positive curvature.

Let $M$ be a simply connected manifold that admits a metric of non-positive curvature. For example take $\mathbb{R}^k\times \mathbb{H}^n$. Take $m+1$ points $x_0$, $x_1, \ldots$ $x_m$, $m>k+1$ and ...