论文标题
地面狄拉克气泡和杀死纺纱器
Ground state Dirac bubbles and Killing spinors
论文作者
论文摘要
我们证明了$ \ mathbb {r}^n $，$ n \ geq2 $的关键dirac方程基态解决方案的分类结果。通过利用其保形协方差，方程可以在圆形球体上构成$ \ mathbb {s}^n $，而在地面上的非零溶液是通过杀死旋转器来给出的，直到保形差异性。此外，关键狄拉克方程的这种基态解决方案也与球体的Yamabe方程有关，为此我们至关重要地利用了一些已知的分类结果。
We prove a classification result for ground state solutions of the critical Dirac equation on $\mathbb{R}^n$, $n\geq2$. By exploiting its conformal covariance, the equation can be posed on the round sphere $\mathbb{S}^n$ and the non-zero solutions at the ground level are given by Killing spinors, up to conformal diffeomorphisms. Moreover, such ground state solutions of the critical Dirac equation are also related to the Yamabe equation for the sphere, for which we crucially exploit some known classification results.
