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Coupling perturbations of the conformal Einstein-Dirac system on round spheres
Abstract
We study the conformal Einstein-Dirac system on the round sphere Sm, m≥3, with coupling coefficient 1+eps k, where k∈ C2(Sm,R) and eps is small. Morse and degree conditions yield solutions with positive scalar component, and a generic nondegeneracy condition gives multiplicity modulo spinorial symmetries. For a suitable fixed coefficient, we obtain a noncompact solution sequence with infinitely many distinct energy values. A Kazdan-Warner identity gives nonexistence for a smooth Morse potential and its small C2-perturbations, even with positive coupling. The existence proofs use a local reduction in the interior of the positive cone, accommodating the negative powers occurring when m≥5.
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BibTeX
@misc{xu2026coupling,
title = {{Coupling perturbations of the conformal Einstein-Dirac system on round spheres}},
author = {Ke Xu and Tian Xu and Minbo Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32172},
eprint = {2610.32172},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32172},
}
RIS
TY - UNPB
TI - Coupling perturbations of the conformal Einstein-Dirac system on round spheres
AU - Ke Xu
AU - Tian Xu
AU - Minbo Yang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32172
UR - https://arxiv.org/abs/2610.32172
AB - We study the conformal Einstein-Dirac system on the round sphere S^m, m≥3, with coupling coefficient 1+eps k, where k∈ C^2(S^m,R) and eps is small. Morse and degree conditions yield solutions with positive scalar component, and a generic nondegeneracy condition gives multiplicity modulo spinorial symmetries. For a suitable fixed coefficient, we obtain a noncompact solution sequence with infinitely many distinct energy values. A Kazdan-Warner identity gives nonexistence for a smooth Morse potential and its small C^2-perturbations, even with positive coupling. The existence proofs use a local reduction in the interior of the positive cone, accommodating the negative powers occurring when m≥5.
ER -