Abstract
We discuss the existence of the angle between two curves in Teichmüller spaces and show that, in any infinite dimensional Teichmüller space, there exist infinitely many geodesic triangles each of which has the same three vertices and satisfies the property that its three sides have the same and arbitrarily given length while its three angles are equal to any given three possibly different numbers from 0 to \(\pi \). This implies that the sum of three angles of a geodesic triangle may be equal to any given number from 0 to \(3\pi \) in an infinite dimensional Teichmüller space.
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The authors would like to thank the referee for useful advice.
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Research supported by the National Natural Science Foundation of China and the Specialized Research Fund for the Doctoral Program of Higher Education of China.
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Hu, Y., Shen, Y. On angles in Teichmüller spaces. Math. Z. 277, 181–193 (2014). https://doi.org/10.1007/s00209-013-1249-3
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DOI: https://doi.org/10.1007/s00209-013-1249-3