Singular solutions of the Yamabe problem in the Heisenberg group and their bifurcation
Abstract
We prove the existence of a homogeneous singular solution of the critical equation $$-Δu = u^{\frac{Q+2}{Q-2}}$$ on the Heisenberg group $H^n$, where $Q$ is the \textit{homogeneous dimension}. In order to do this, we introduce a suitable concept of normal curvature for hypersurfaces. Furthermore we study the bifurcation of non-homogeneous solutions from the homogeneous one.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- Publisher
- Scuola Normale Superiore - Edizioni della Normale
- Pages
- 19–19
- Publication date
- 12 January 2026
- Language
- EN