发表机构
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分类了十五维八元数海森堡群上Yamabe型方程的有限能量正解，显式描述Folland-Stein-Sobolev不等式的极值函数，证实了Garofalo和Vassilev的猜想。
AI 中文摘要
我们分类了十五维八元数海森堡群上Yamabe型方程的有限能量正解，该群的代数是非结合的。该群上Folland-Stein-Sobolev不等式的极值函数被显式描述。这证实了Garofalo和Vassilev [Duke Math. J. 2001] 在十五维八元数海森堡群上的猜想。
英文摘要
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.
CommentsSubmitted to a journal, currently under review
