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arXiv · 2003.03949

Ground state Dirac bubbles and Killing spinors

William Borrelli·Andrea Malchiodi·Ruijun Wu
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Abstract

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.

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William Borrelli, Andrea Malchiodi, Ruijun Wu. 2020-03-09. Ground state Dirac bubbles and Killing spinors. https://doi.org/10.1007/s00220-021-04013-1

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