2 problems

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The conjecture that the cut time equals the first coordinate cut time on Grushin spaces
Cut-time conjecture. The cut time $t_{\operatorname{cut}}$ is identically
Conjectureopengeodesics grushin-spaces sub-riemannian-geometryarXiv posted 2 days ago
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Bi-Lipschitz embeddability conjecture for extended spaces of Grushin type
Let $n,l\in\mathbb N$ , and let the extended space of Grushin type be $\mathbb R^n\times\mathbb R^l$ equipped with the Carnot–Carathéodory distance associated to the horizontal dist…
Conjectureopenbi-lipschitz-embeddings grushin-spaces metric-geometryarXiv posted 2 days ago

The conjecture that the cut time equals the first coordinate cut time on Grushin spaces