Singular solutions of the Yamabe problem in the Heisenberg group and their bifurcation

Claudio Afeltra

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arXiv · 2012.12706

Singular solutions of the Yamabe problem in the Heisenberg group and their bifurcation

Claudio Afeltra

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Abstract

We prove the existence of a homogeneous singular solution of the critical equation $$-\Delta u = u^{\frac{Q+2}{Q-2}}$$ 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.

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Claudio Afeltra. 2020-12-23. Singular solutions of the Yamabe problem in the Heisenberg group and their bifurcation. https://arxiv.org/abs/2012.12706

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