Euclidean triangulated surface .Tl;M/ characterizes a polyhedral metric with conical singularities associated with the vertices of the triangulation. In this chapter we show that around any such a vertex we can introduce complex coordinates in terms of which we can write down the conformal conical metric, locally parametrizing the singular structure of .Tl;M/. This makes available a powerful dictionary between 2–dimensional triangulations and complex geometry.
Singular euclidean structures and riemann surfaces
Carfora, Mauro;Marzuoli, Annalisa
2017-01-01
Abstract
Euclidean triangulated surface .Tl;M/ characterizes a polyhedral metric with conical singularities associated with the vertices of the triangulation. In this chapter we show that around any such a vertex we can introduce complex coordinates in terms of which we can write down the conformal conical metric, locally parametrizing the singular structure of .Tl;M/. This makes available a powerful dictionary between 2–dimensional triangulations and complex geometry.File in questo prodotto:
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