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arXiv · 2609.17072

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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Daowen Lin. 2026-09-15. Classification of finite energy positive solutions to Yamabe-type equation on the fifteen dimensional octonionic Heisenberg group. https://arxiv.org/abs/2609.17072

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