论文标题
扩展和改进锥形双汤
Extending and improving conical bicombings
论文作者
论文摘要
我们研究了接收圆锥形双栓的度量空间，从而遵守一种弱的非阳性曲率形式。此类空间的主要示例是注入性度量空间。在本文中，我们通过证明每个这样的空间都是等距的，对某些注射度度量空间的封闭$σ$ -CONVEX子集进行等等速线，从而使完整的度量空间完全表征完整的圆锥形双空间。此外，我们表明，接收圆锥形双栓的每个合适的度量空间也承认满足某些凸条件的一致性双栓。这可以看作是一种有力的迹象，即从下降和朗提出的关于改善圆锥体两组的问题可能有积极的答案。作为一个应用程序，我们证明，任何在适当的度量空间上使用圆锥形双栓的群体都允许$ \ MATHCAL {Z} $ - 结构。
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.
