论文标题
海森伯格集团雅马布问题的单数解决方案及其分叉
Singular solutions of the Yamabe problem in the Heisenberg group and their bifurcation
论文作者
论文摘要
我们证明存在关键方程式$$的均匀单数解 - ΔU= u^{\ frac {q+2} {q-2} {q-2}} $$在Heisenberg $ h^n $上，其中$ q $是\ textit {pextit {均值{均质尺寸}。为了做到这一点，我们为Hypersurfaces引入了适当的正常曲率概念。此外，我们研究了同质溶液的非均匀溶液的分叉。
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.
