PreprintCC BY 4.0arXiv
Geometrically distinct unbounded continua of solutions for Yamabe-type equations
Abstract
We study global bifurcation for Yamabe-type equations on closed Riemannian manifolds with symmetries. For isometric group actions with interval orbit space and a suitable range of exponents, we prove the existence of pairwise disjoint unbounded continua bifurcating from the positive eigenvalues of the Laplace--Beltrami operator that admit invariant eigenfunctions. All nontrivial solutions in these continua change sign. The results cover critical and some supercritical exponents. On spheres and complex and quaternionic projective spaces, we obtain lower bounds on the number of geometrically distinct continua bifurcating from the same eigenvalue.
Related
- Nonuniqueness of Solutions to 2D Incompressible Euler Equations with Unbounded Vorticity
- Lyapunov-Krasovsky Functionals and the Existence of Unbounded Solutions of Functional-Differential Equations of Retarded Type
- Aleksandrov-Bakelman-Pucci maximum principle for Ln-viscosity solutions of uniformly elliptic equations with unbounded terms: The critical case
- Fundamental solutions to Kolmogorov-Fokker-Planck equations with unbounded lower order terms
- Unbounded variation solutions for uniformly elliptic equations in nondivergence form in dimension three
BibTeX
@misc{stefaniak2026geometrically,
title = {{Geometrically distinct unbounded continua of solutions for Yamabe-type equations}},
author = {Piotr Stefaniak},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03292},
eprint = {2610.03292},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03292},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometrically distinct unbounded continua of solutions for Yamabe-type equations
AU - Piotr Stefaniak
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03292
UR - https://arxiv.org/abs/2610.03292
AB - We study global bifurcation for Yamabe-type equations on closed Riemannian manifolds with symmetries. For isometric group actions with interval orbit space and a suitable range of exponents, we prove the existence of pairwise disjoint unbounded continua bifurcating from the positive eigenvalues of the Laplace--Beltrami operator that admit invariant eigenfunctions. All nontrivial solutions in these continua change sign. The results cover critical and some supercritical exponents. On spheres and complex and quaternionic projective spaces, we obtain lower bounds on the number of geometrically distinct continua bifurcating from the same eigenvalue.
ER -