ANGLE GEOMETRY IN THE UNIVERSAL TEICHMULLER SPACE

作者：Fan Jinhua^*; Jiang Yunping

来源：Proceedings of the American Mathematical Society, 2015, 143(4): 1651-1659.

• Teichmuller distance
• geodesic segment
• inner angle

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 pi, the second example has the sum of the three angles equal to pi, and the third example has the sum of the three angles greater than pi. 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.

• 出版日期2015-4
• 单位南京大学