Year: 2026
Type: preprint
Abstract: We prove sharp improved Sobolev inequalities on $\mathbb{S}^n$, $n\ge 4$, for functions whose critical density $|u|^{2n/(n-2)}$ has zero barycenter, without any symmetry assumption. The Dirichlet coefficient improves by the optimal factor $2^{-2/n}$, while the coefficient of the $L^2$ term remains one. Equality holds precisely for constant functions. This establishes the sharp form of Aubin's improved Sobolev inequality in every dimension $n\ge4$.
Source: arXiv (Cornell University)
Authors: Wei, Juncheng, Yan, Zetian, Ye, Zikai
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222959461