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Isometric embeddings of Teichm\"uller spaces are covering constructions

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arxiv 2305.04153 v1 pith:UK2BUKKB submitted 2023-05-07 math.GT math.AGmath.CV

Frederik Benirschke , Carlos A. Serván This is my paper · ORCID
classification math.GTmath.AGmath.CV
keywords isometricteichmullercoveringembeddingsspacesbranchedconsequence
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abstract

Pulling back complex structures along a branched covering induces a holomorphic isometric embedding of Teichm\"uller spaces. We show that for dimension at least $2$, all isometric embeddings arise from branched coverings. This generalizes a theorem of Royden. As a consequence we obtain that totally geodesic submanifolds of Teichm\"uller space, which are isometric to some Teichm\"uller space, are covering constructions. Another consequence is the classification of locally isometric embeddings of moduli spaces of Riemann surfaces.

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  1. The geometry of totally geodesic subvarieties of moduli spaces of Riemann surfaces

    math.GT 2024-12 conditional novelty 8.0 of 10

    Totally geodesic subvarieties of moduli space have semisimple Deligne-Mumford boundary and are hierarchically hyperbolic.

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