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Results tagged with mg.metric-geometry
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user 10583
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
10
votes
4
answers
1k
views
Geodesic path on the unit sphere with the sup norm
Let $X$ be the unit sphere of $\mathbb{R}^n$ with the sup norm, i.e. $X=\{x\in\mathbb{R}^n: \|x\|_{\infty}=1\}$. Let the metric $d$ on $X$ be the geodesic metric induced by the sup norm, i.e for any …
- 744
7
votes
1
answer
361
views
Nonexpansive multi-valued maps in $\ell^2$
Let $C$ be a nonempty bounded closed convex subset, say the unit ball, of $\ell^2(\mathbb{N})$. Let $T: C\to 2^C$ be a map such that $T(x)$ is nonempty closed for each $x$, and that $$D(Tx,Ty)\le \|x- …
- 744