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Totally geodesic submanifolds of Teichmüller space
Journal of Differential Geometry  (IF2.688),  Pub Date : 2020-07-01, DOI: 10.4310/jdg/1594260019
Alex Wright

We show that any totally geodesic submanifold of Teichmuller space of dimension greater than one covers a totally geodesic subvariety, and only finitely many totally geodesic subvarieties of dimension greater than one exist in each moduli space.