On the Moduli Space of Singular Euclidean Surfaces

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The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.
To appear in the Handbook of Teichmuller Theory, vol. 1, ed. A. Papadopoulos, European Math. Society Series, 2007

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