Accepted Paper

Inserted: 30 jul 2023
Last Updated: 29 jul 2026

Journal: Math. Ann.
Year: 2026

Abstract:

We study the loss of compactness for optimal functions of a subcritical approximations of the sharp Folland-Stein-Sobolev embedding in the Heisenberg group. When blow-up is prevent at the boundary we show that centered-symmetric maximizers in a Kor\'any ball concentrate at its center. Moreover, we obtain the exact blow-up rate and the pointwise asymptotic profile away from the pole, in turn establishing a natural counterpart of the classical Brezis and Peletier asymptotics for nearly critical Sobolev problems.

Keywords: Heisenberg group, Sobolev embeddings, CR Yamabe

Download:

• PP26-asymp-CR.pdf