A Bounded Convex Hilbert Domain with Vanishing Squeezing
Manuscript 19 October 2026 · Online 19 October 2026
Abstract
We construct a bounded convex balanced domain in the complex Hilbert space C direct-sum ell^2 that is not holomorphic homogeneous regular. The domain is Omega = {(z,w): |z| + ||w||_infinity < 1, ||w||_2 < 1}. Its squeezing function at (t,0) is bounded above and below by positive constant multiples of 1-t as t increases to 1. The upper bound follows from explicit holomorphic retractions onto polydiscs of increasing dimension and an elementary Hilbert-space Schwarz argument. This gives a negative answer to Question 5 in Kim's 2018 Oberwolfach report. No boundary smoothness is claimed, and the separate Question 6 about squeezing constants of arbitrary bounded homogeneous domains is not addressed. This is an AI-assisted, self-audited, unrefereed preprint; no external review, formal verification or absolute priority is claimed.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete counterexample to Question 5
- Categories
- math.CV · math.FA
- Manuscript
- 19 October 2026
- Online release
- 19 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “A Bounded Convex Hilbert Domain with Vanishing Squeezing,” EulerSolve Research Papers, OWR-16412-006, 2026. https://doi.org/10.5281/zenodo.23461147.
BibTeX
@misc{ferudun2026hilbertsqueezing,
author = {Ferudun, Alper},
title = {A Bounded Convex Hilbert Domain with Vanishing Squeezing},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/owr-16412-006/},
doi = {10.5281/zenodo.23461147},
note = {OWR-16412-006; unrefereed preprint}
}