论文标题
低氧尺寸的大地测量空间
Geodesic spaces of low Nagata dimension
论文作者
论文摘要
我们表明，每个测量公制空间都承认注射式连续地图进入平面，并且每个平面图最多都具有Nagata尺寸，因此最多渐近的维度。这依靠并回答了Fujiwara和Papasoglu的最新作品中的一个问题。我们得出的结论是，所有三维Hadamard歧管都有Nagata维度三。结果，所有这些歧管都是绝对的Lipschitz缩回。
We show that every geodesic metric space admitting an injective continuous map into the plane as well as every planar graph has Nagata dimension at most two, hence asymptotic dimension at most two. This relies on and answers a question in a very recent work by Fujiwara and Papasoglu. We conclude that all three-dimensional Hadamard manifolds have Nagata dimension three. As a consequence, all such manifolds are absolute Lipschitz retracts.
