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PreprintCC BY 4.0arXiv

Classification of finite energy positive solutions to Yamabe-type equation on the fifteen dimensional octonionic Heisenberg group

  • Daowen Lin
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Abstract

We classify finite-energy positive solutions to the Yamabe-type equation on the 15-dimensional octonionic Heisenberg group, whose algebra is non-associative. Extremals for the Folland-Stein-Sobolev inequality on this group are explicitly described. This confirms the conjecture of Garofalo and Vassilev [Duke Math. J. 2001] on the $15$ dimensional octonionic Heisenberg group.

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Cite

BibTeXRIS
BibTeX
@misc{lin2026classification,
  title = {{Classification of finite energy positive solutions to Yamabe-type equation on the fifteen dimensional octonionic Heisenberg group}},
  author = {Daowen Lin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17072},
  eprint = {2609.17072},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17072},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Classification of finite energy positive solutions to Yamabe-type equation on the fifteen dimensional octonionic Heisenberg group
AU  - Daowen Lin
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17072
UR  - https://arxiv.org/abs/2609.17072
AB  - We classify finite-energy positive solutions to the Yamabe-type equation on the 15-dimensional octonionic Heisenberg group, whose algebra is non-associative. Extremals for the Folland-Stein-Sobolev inequality on this group are explicitly described. This confirms the conjecture of Garofalo and Vassilev [Duke Math. J. 2001] on the $15$ dimensional octonionic Heisenberg group.
ER  -