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Totally Geodesic Submanifolds of Teichmüller Space in Complex Dimension at Least Three
Let $N\subset \mathcal{T}_{g,n}$ be a connected complex totally geodesic submanifold. We prove that if $\dim_{\mathbb{C}}N\ge3$, then $N$ is the image of an entire Teichmüller space under a covering construction induced by a finite branched cover of marked surfaces. This answers a question of Arana-
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