PreprintCC BY 4.0arXiv
Singular Yamabe metrics on complements of closed sets
Abstract
Let n≥3 and let Λ⊂ 𝕊n be closed, contain at least two points, and satisfy dimHΛ<(n−2)/2. We prove that there exists a complete metric of scalar curvature n(n−1) on 𝕊 n∖Λ, conformal to the round metric.
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BibTeX
@misc{li2026singular,
title = {{Singular Yamabe metrics on complements of closed sets}},
author = {Weiyang Li and Heng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21963},
eprint = {2610.21963},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21963},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Singular Yamabe metrics on complements of closed sets
AU - Weiyang Li
AU - Heng Zhang
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21963
UR - https://arxiv.org/abs/2610.21963
AB - Let n≥3 and let Λ⊂ 𝕊^n be closed, contain at least two points, and satisfy dim_HΛ<(n−2)/2. We prove that there exists a complete metric of scalar curvature n(n−1) on 𝕊 ^n∖Λ, conformal to the round metric.
ER -