PreprintCC BY 4.0arXiv
Quantitative finiteness for maximal complex totally geodesic submanifolds of non-arithmetic ball quotients
Abstract
We prove that the number of maximal complex totally geodesic submanifolds of a smooth finite-volume non-arithmetic ball quotient is bounded linearly by its volume, with a constant depending only on the complex dimension. This gives a quantitative strengthening of the finiteness theorems of Bader--Fisher--Miller--Stover (Invent. Math., 2023) and Baldi--Ullmo (Ann. of Math., 2023).
Related
- Totally Geodesic Submanifolds of Teichmüller Space in Complex Dimension at Least Three
- Arithmeticity, superrigidity, and totally geodesic submanifolds of infinite-volume hyperbolic manifolds
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- Arakelov inequalities and characterization of totally geodesic ball quotients in 𝒜g
- A finiteness theorem for geodesic Leech wheels
BibTeX
@misc{hu2026quantitative,
title = {{Quantitative finiteness for maximal complex totally geodesic submanifolds of non-arithmetic ball quotients}},
author = {Tianzhi Hu and Runze Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03514},
eprint = {2611.03514},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03514},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantitative finiteness for maximal complex totally geodesic submanifolds of non-arithmetic ball quotients
AU - Tianzhi Hu
AU - Runze Zhang
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03514
UR - https://arxiv.org/abs/2611.03514
AB - We prove that the number of maximal complex totally geodesic submanifolds of a smooth finite-volume non-arithmetic ball quotient is bounded linearly by its volume, with a constant depending only on the complex dimension. This gives a quantitative strengthening of the finiteness theorems of Bader--Fisher--Miller--Stover (Invent. Math., 2023) and Baldi--Ullmo (Ann. of Math., 2023).
ER -