A Parametrization of Solutions to the Yamabe Equation with Isolated Singularity

@misc{han2026parametrization,
  title = {{A Parametrization of Solutions to the Yamabe Equation with Isolated Singularity}},
  author = {Qing Han and Jui-Yun Hung and Nan Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19984},
  eprint = {2610.19984},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19984},
}

TY  - UNPB
TI  - A Parametrization of Solutions to the Yamabe Equation with Isolated Singularity
AU  - Qing Han
AU  - Jui-Yun Hung
AU  - Nan Wu
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19984
UR  - https://arxiv.org/abs/2610.19984
AB  - Inspired by a pioneering work by Caffarelli, Gidas, and Spruck, we study positive solutions to the Yamabe equation with nonremovable isolated singularities. It is known that there is a formal one-to-one correspondence between the collection of the solutions to the Yamabe equation with nonremovable isolated singularities and the collection of harmonic functions through formal infinite series determined by the harmonic functions. In this paper, we prove that these formal infinite series yield actual solutions to the Yamabe equation with a nonremovable isolated singularity. These solutions to the Yamabe equation have designated asymptotic behaviors determined by the harmonic functions. In a broader context, we provide a general method of constructing all solutions near their isolated singular points and all solutions near infinity.
ER  -