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YCor
YCor
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Hyperbolic Space Embedsspace embeds into Wasserstein Spacespace

Fix a positive integer $n$, let $\mathbb{H}^n$ be the $n$-dimensional Hyperbolichyperbolic space, $r>0$, $x\in \mathbb{H}^n$ and consider the closed (compact) geodesic ball $B_{\mathbb{H}^n}(x,r)$. Are there known estimates on the minimum distortion of a bi-Lipschitz embedding of $B_{\mathbb{H}^n}(x,r)$ into $\mathcal{W}_2(\mathbb{R})$.

Let me just note that a bi-Lipschitz embedding into $\mathcal{W}_2(\mathbb{R})$ must exist by this paper.

Hyperbolic Space Embeds Wasserstein Space

Fix a positive integer $n$, let $\mathbb{H}^n$ be the $n$-dimensional Hyperbolic space, $r>0$, $x\in \mathbb{H}^n$ and consider the closed (compact) geodesic ball $B_{\mathbb{H}^n}(x,r)$. Are there known estimates on the minimum distortion of a bi-Lipschitz embedding of $B_{\mathbb{H}^n}(x,r)$ into $\mathcal{W}_2(\mathbb{R})$.

Let me just note that a bi-Lipschitz embedding into $\mathcal{W}_2(\mathbb{R})$ must exist by this paper.

Hyperbolic space embeds into Wasserstein space

Fix a positive integer $n$, let $\mathbb{H}^n$ be the $n$-dimensional hyperbolic space, $r>0$, $x\in \mathbb{H}^n$ and consider the closed (compact) geodesic ball $B_{\mathbb{H}^n}(x,r)$. Are there known estimates on the minimum distortion of a bi-Lipschitz embedding of $B_{\mathbb{H}^n}(x,r)$ into $\mathcal{W}_2(\mathbb{R})$.

Let me just note that a bi-Lipschitz embedding into $\mathcal{W}_2(\mathbb{R})$ must exist by this paper.

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Carlos_Petterson
Carlos_Petterson
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Hyperbolic Space Embeds Wasserstein Space

Fix a positive integer $n$, let $\mathbb{H}^n$ be the $n$-dimensional Hyperbolic space, $r>0$, $x\in \mathbb{H}^n$ and consider the closed (compact) geodesic ball $B_{\mathbb{H}^n}(x,r)$. Are there known estimates on the minimum distortion of a bi-Lipschitz embedding of $B_{\mathbb{H}^n}(x,r)$ into $\mathcal{W}_2(\mathbb{R})$.

Let me just note that a bi-Lipschitz embedding into $\mathcal{W}_2(\mathbb{R})$ must exist by this paper.