Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2504.14182 |
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Sommario:
- We study Yamabe-type equations on the product of two spheres $(S^n \times S^n, G_δ)$, where $G_δ$ is a family of Riemannian metrics parametrized by $δ> 0$. Using bifurcation theory and isoparametric functions, we establish the existence of degenerate solutions that are invariant under the diagonal action of $O(n+1)$ and depend non-trivially on both factors. Our analysis relies on the properties of Gegenbauer polynomials and a careful application of local bifurcation techniques for simple eigenvalues. These results extend previous studies by demonstrating the emergence of solutions that do not solely depend on a single factor, thereby providing new insights into the structure of solutions for Yamabe-type problems on product manifolds.