PreprintarXiv licencearXiv
The Bloch constant is strictly smaller than the Ahlfors--Grunsky value
Abstract
We prove that the classical Bloch constant is strictly smaller than the Ahlfors--Grunsky value, disproving the famous Bloch constant conjecture. The Lean 4 formalization of the main results are also provided.
Related
- Bounds for the univalent Bloch-Landau constant
- The Dirichlet problem with boundary data of fractional smoothness in domains with Ahlfors regular boundary
- Sharp Higher Integrability Theory, Part I: The Lp-norm of the Beurling--Ahlfors transform
- Decomposition of functions of bounded variation in Ahlfors-regular PI spaces
- Sumsets of Ahlfors--David regular sets
BibTeX
@misc{zhang2026bloch,
title = {{The Bloch constant is strictly smaller than the Ahlfors--Grunsky value}},
author = {Teng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16808},
eprint = {2610.16808},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16808},
}
RIS
TY - UNPB
TI - The Bloch constant is strictly smaller than the Ahlfors--Grunsky value
AU - Teng Zhang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16808
UR - https://arxiv.org/abs/2610.16808
AB - We prove that the classical Bloch constant is strictly smaller than the Ahlfors--Grunsky value, disproving the famous Bloch constant conjecture. The Lean 4 formalization of the main results are also provided.
ER -