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Busemann G-spaces with convex balls
Abstract
We prove that any Busemann G-space such that every sufficiently small metric ball is convex is a topological manifold. The key ingredient in the proof is Ivanov's Helly theorem. The appendix contains a counterexample to a question of Berestovskii--Halverson--Repovš.
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BibTeX
@misc{fujioka2026busemann,
title = {{Busemann G-spaces with convex balls}},
author = {Tadashi Fujioka and Shijie Gu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.20800},
eprint = {2608.20800},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20800},
}
RIS
TY - UNPB
TI - Busemann G-spaces with convex balls
AU - Tadashi Fujioka
AU - Shijie Gu
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.20800
UR - https://arxiv.org/abs/2608.20800
AB - We prove that any Busemann G-space such that every sufficiently small metric ball is convex is a topological manifold. The key ingredient in the proof is Ivanov's Helly theorem. The appendix contains a counterexample to a question of Berestovskii--Halverson--Repovš.
ER -