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Totally Geodesic Submanifolds of Teichmüller Space in Complex Dimension at Least Three

  • Longsong Jia
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Abstract

Let N⊂ 𝒯g,n be a connected complex totally geodesic submanifold. We prove that if dimℂN≥3, 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-Herrera and Wright.

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Cite

BibTeXRIS
BibTeX
@misc{jia2026totally,
  title = {{Totally Geodesic Submanifolds of Teichmüller Space in Complex Dimension at Least Three}},
  author = {Longsong Jia},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15602},
  eprint = {2609.15602},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15602},
}
RIS
TY  - UNPB
TI  - Totally Geodesic Submanifolds of Teichmüller Space in Complex Dimension at Least Three
AU  - Longsong Jia
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15602
UR  - https://arxiv.org/abs/2609.15602
AB  - Let N⊂ 𝒯_g,n be a connected complex totally geodesic submanifold. We prove that if dim_ℂN≥3, 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-Herrera and Wright.
ER  -