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arXiv · 2301.03757

Constructions of Delaunay-type solutions for the spinorial Yamabe equation on spheres

Ali Maalaoui·Yannick Sire·Tian Xu
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Abstract

In this paper we construct singular solutions to the critical Dirac equation on spheres. More precisely, first we construct solutions admitting two points singularities that we call Delaunay-type solutions because of their similarities with the Delaunay solutions constructed for the singular Yamabe problem in \cite{MP1 , Schoen1989}. Then we construct another kind of singular solutions admitting a great circle as a singular set. These solutions are the building blocks for singular solutions on a general Spin manifold.

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Ali Maalaoui, Yannick Sire, Tian Xu. 2023-01-10. Constructions of Delaunay-type solutions for the spinorial Yamabe equation on spheres. https://arxiv.org/abs/2301.03757

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