Calculus of Variations and Geometric Measure Theory
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W. Borrelli - A. Malchiodi - R. Wu

Ground state Dirac bubbles and Killing spinors

created by malchiodi on 09 Mar 2020
modified by borrelli on 15 Feb 2021

[BibTeX]

Published Paper

Inserted: 9 mar 2020
Last Updated: 15 feb 2021

Journal: Commun. Math. Phys.
Pages: 30
Year: 2021
Doi: https://doi.org/10.1007/s00220-021-04013-1

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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