论文标题
非物性弯曲空间的圆周延伸图
Circumcenter extension maps for non-positively curved spaces
论文作者
论文摘要
我们表明，只要歧管满足一定的可见性条件，就可以在哈达姆歧管的边界之间保存同构的每个交叉比例延伸到一个称为圆周延伸的连续图。我们表明，每当歧管通过等轴形成允许的coCocompact动作，并且我们改善了比斯瓦斯在CAT（-1）}空间的情况下改善BISWAS提供的准iSomemotry常数。最后，我们提供了足够的条件，使该地图成为Hadamard表面的等轴测图。
We show that every cross ratio preserving homeomorphism between boundaries of Hadamard manifolds extends to a continuous map, called circumcenter extension, provided that the manifolds satisfy certain visibility conditions. We show that this map is a rough isometry, whenever the manifolds admit cocompact group actions by isometries and we improve the quasi-isometry constants provided by Biswas in the case of CAT(-1)} spaces. Finally, we provide a sufficient condition for this map to be an isometry in the case of Hadamard surfaces.
