PreprintCC BY 4.0arXiv
New examples of tame families of Stein manifolds
Abstract
Let X be a smooth open manifold of even dimension, T be a topological space, and {Jt}t∈ T be a continuous family of smooth integrable Stein structures on X. The family is said to be tame if the Jt-convex hulls of any compact set in X are upper semicontinuous with respect to t∈ T. It was recently shown that tame Stein families have good function-theoretic properties; in particular, they satisfy the Oka principle for families of holomorphic maps to any Oka manifold. We analyse some constructions and operations on Stein manifolds that preserve tameness of families and we exhibit several conceptually new examples of tame Stein families.
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BibTeX
@misc{forstneric2026examples,
title = {{New examples of tame families of Stein manifolds}},
author = {Franc Forstneric and Finnur Larusson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24484},
eprint = {2609.24484},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24484},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New examples of tame families of Stein manifolds
AU - Franc Forstneric
AU - Finnur Larusson
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.24484
UR - https://arxiv.org/abs/2609.24484
AB - Let X be a smooth open manifold of even dimension, T be a topological space, and {J_t}_t∈ T be a continuous family of smooth integrable Stein structures on X. The family is said to be tame if the J_t-convex hulls of any compact set in X are upper semicontinuous with respect to t∈ T. It was recently shown that tame Stein families have good function-theoretic properties; in particular, they satisfy the Oka principle for families of holomorphic maps to any Oka manifold. We analyse some constructions and operations on Stein manifolds that preserve tameness of families and we exhibit several conceptually new examples of tame Stein families.
ER -