Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.17072

Author: Lin, Daowen

Institution: Okinawa Institute of Science and Technology Graduate University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213396311

Cites: 3

Cited by: 1

Related to: 10