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\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

2. Uniform and Coarse Embeddings


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      Problem 2.1.

      [Alexandros Eskenazis] Suppose $X$ is a Banach space that coarsely contains every locally finite metric space. Does $X$ have trivial cotype?


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          Problem 2.2.

          [Guoliang Yu] Does every metric space of bounded geometry admit a coarse embedding into a (possibly infinite dimensional) CAT(0) space? Does every finitely generated group admit such an embedding?


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              Problem 2.3.

              [Florent Baudier] Let $q \in (2,\infty)$. Does $L_q$ admit a coarse or uniform embedding into $\ell_q$?


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                  Problem 2.4.

                  [Assaf Naor] Let $q \in (2,\infty)$. Does $(L_q,\|\cdot\|^{\frac12})$ admit a biLipschitz embedding into $L_q$?


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                      Problem 2.5.

                      [Bruno de Mendonça Braga] Is there a bounded geometry space that coarsely contains every bounded geometry space? Is there a bounded geometry space with Property A that coarsely contains every bounded geometry space with Property A?


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                          Problem 2.6.

                          [Guoliang Yu] Is it true that for every bounded degree graph $G$, there exists a finitely generated group that coarsely contains $G$?


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                              Problem 2.7.

                              [Florent Baudier] Does the unit ball of every superreflexive Banach space uniformly embed into some Hilbert space?

                                  Cite this as: AimPL: Metric embeddings, available at http://aimpl.org/metricembeddings.