扩展与改进锥形双梳（conical bicombings）
Extending and improving conical bicombings
AI总结：
本文刻画允许锥形双梳的完备度量空间，证明其等距于内射度量空间的闭σ-凸子集，并在真空间情形构造满足凸性条件的一致双梳，进而得到几何作用群的Z-结构。
摘要：
我们研究允许锥形双梳（conical bicombing）并因此服从弱形式非正曲率的度量空间。这类空间的主要例子是内射度量空间。在本文中，我们通过证明每个这样的空间都与某个内射度量空间的一个闭 σ-凸子集等距，给出了允许锥形双梳的完备度量空间的完整刻画。此外，我们证明每个允许锥形双梳的真度量空间也允许一个满足某些凸性条件的一致双梳（consistent bicombing）。这可被视为一个强烈迹象，表明 Descombes 和 Lang 提出的关于改进锥形双梳的问题可能有肯定答案。作为应用，我们证明任何在具有锥形双梳的真度量空间上几何作用的群都允许一个 Z-结构。
英文摘要：
We study metric spaces that admit a conical bicombing and thus obey a weak form of non-positive curvature. Prime examples of such spaces are injective metric spaces. In this article we give a complete characterization of complete metric spaces admitting a conical bicombing by showing that every such space is isometric to a closed $σ$-convex subset of some injective metric space. In addition, we show that every proper metric space that admits a conical bicombing also admits a consistent bicombing that satisfies certain convexity conditions. This can be seen as a strong indication that a question from Descombes and Lang about improving conical bicombings might have a positive answer. As an application, we prove that any group acting geometrically on a proper metric space with a conical bicombing admits a $\mathcal{Z}$-structure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
