Presented By: Geometry Seminar - Department of Mathematics
Isometric embeddings of Teichmuller spaces
Carlos Servan
A classical theorem of Royden states that any biholomorphism or isometry of Teichmuller space of closed surfaces, is induced by a homeomorphism of the underlying surface. Over the years, this result has been generalized in a variety of ways. Such as, to arbitrary surfaces of non-exceptional type or relaxing isometries to quasi-isometries. In this talk, we will discuss another generalization. We will consider isometric embeddings between Teichmuller spaces of finite type surfaces and show that besides some low-dimensional cases, they are induced by branched coverings between the underlying surfaces. As a consequence, we obtain a classification of local isometric embeddings between moduli spaces of curves. This is joint work with Frederik Benirschke.
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