Angle geometry in the universal Teichmüller space
Angle geometry in the universal Teichmüller space
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DOI：
10.1090/s0002-9939-2014-12352-5
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发表时间：
2014-11
期刊：
影响因子：
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通讯作者：
Jinhua Fan;Yunping Jiang
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文献类型：
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作者：
Jinhua Fan;Yunping Jiang
本文研究泛Teichmuller空间中的角几何。我们构造了三个由测地线线段包围的三角形的例子，使得第一个例子的三个内角之和小于π，第二个例子的三个内角之和等于π，第三个例子的三个内角之和大于π。我们的结果否定地回答了钟立和易琦提出的一个问题。此外，我们的结果表明，普遍的Teichmuller空间的所有双曲，欧几里德，和球形的现象，在角几何。
In this paper we investigate angle geometry in the universal Teichmuller space. We construct three examples of triangles bounded by geodesic segments such that the first example has the sum of the three inner angles less than π, the second example has the sum of the three angles equal to π, and the third example has the sum of the three angles greater than π. Our result gives a negative answer to a problem raised by Zhong Li and Yi Qi. Moreover, our results indicate that the universal Teichmuller space presents all hyperbolic, Euclidean, and spherical phenomena in angle geometry.