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A conjugate radius bound for open three-manifolds
Abstract
We prove that every complete, connected, noncompact Riemannian three-manifold without boundary with scalar curvature at least $6$ has conjugate radius at most 2π/3. This resolves Shen's conjecture on the strict conjugate-radius bound conj(M,g)<π in dimension three.
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BibTeX
@misc{ge2026conjugate,
title = {{A conjugate radius bound for open three-manifolds}},
author = {Jian Ge and Chuanhuan Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09773},
eprint = {2610.09773},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09773},
}
RIS
TY - UNPB
TI - A conjugate radius bound for open three-manifolds
AU - Jian Ge
AU - Chuanhuan Li
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09773
UR - https://arxiv.org/abs/2610.09773
AB - We prove that every complete, connected, noncompact Riemannian three-manifold without boundary with scalar curvature at least $6$ has conjugate radius at most 2π/3. This resolves Shen's conjecture on the strict conjugate-radius bound conj(M,g)<π in dimension three.
ER -