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Local convexity obstructions for bounded realizations of Teichmüller space
Abstract
Let D⊂ℂn, n≥2, be a bounded domain that is biholomorphic to a finite-dimensional Teichmüller space. We prove that ∂ D has no locally convex boundary patch containing a complex (n−1)-dimensional manifold through each of its points. Note that in complex dimension two this excludes every locally convex boundary point, without any boundary regularity assumption. In every dimension, we also exclude locally convex C2 boundary patches.
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BibTeX
@misc{liu2026local,
title = {{Local convexity obstructions for bounded realizations of Teichmüller space}},
author = {Jinsong Liu and Xingsi Pu and Lang Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04653},
eprint = {2611.04653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04653},
}
RIS
TY - UNPB
TI - Local convexity obstructions for bounded realizations of Teichmüller space
AU - Jinsong Liu
AU - Xingsi Pu
AU - Lang Wang
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04653
UR - https://arxiv.org/abs/2611.04653
AB - Let D⊂ℂ^n, n≥2, be a bounded domain that is biholomorphic to a finite-dimensional Teichmüller space. We prove that ∂ D has no locally convex boundary patch containing a complex (n−1)-dimensional manifold through each of its points. Note that in complex dimension two this excludes every locally convex boundary point, without any boundary regularity assumption. In every dimension, we also exclude locally convex C^2 boundary patches.
ER -