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PreprintCC BY 4.0arXiv

Isolated singularities of solutions to the Yamabe equation in higher dimensions I

  • Zheng-Chao Han
  • Qinfeng Jiang
  • Hua-Yang Wang
  • Jingang Xiong
  • Lei Zhang
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Abstract

We complete, in the general Riemannian setting, the classification of isolated singularities of positive solutions to the Yamabe equation for dimensions 3≤ n≤29, initiated in the flat case by Caffarelli, Gidas, and Spruck in 1989. Precisely, every isolated singularity is either removable or the solution is asymptotic to a Fowler solution. The sharpness of this range is established by counterexamples for every dimension n≥30 in our companion paper.

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Cite

BibTeXRIS
BibTeX
@misc{han2026isolated,
  title = {{Isolated singularities of solutions to the Yamabe equation in higher dimensions I}},
  author = {Zheng-Chao Han and Qinfeng Jiang and Hua-Yang Wang and Jingang Xiong and Lei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.28323},
  eprint = {2609.28323},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28323},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Isolated singularities of solutions to the Yamabe equation in higher dimensions I
AU  - Zheng-Chao Han
AU  - Qinfeng Jiang
AU  - Hua-Yang Wang
AU  - Jingang Xiong
AU  - Lei Zhang
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.28323
UR  - https://arxiv.org/abs/2609.28323
AB  - We complete, in the general Riemannian setting, the classification of isolated singularities of positive solutions to the Yamabe equation for dimensions 3≤ n≤29, initiated in the flat case by Caffarelli, Gidas, and Spruck in 1989. Precisely, every isolated singularity is either removable or the solution is asymptotic to a Fowler solution. The sharpness of this range is established by counterexamples for every dimension n≥30 in our companion paper.
ER  -