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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

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Contractions in convex metric spaces

Let $M \subset \mathbb{R}^n$ be open, bounded and convex and equip $M$ with an unbounded metric $d$ that induces the Euclidean topology. Is there always a map $f : M \to M$ and two constants $C_1 > 0$ …
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