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arXiv · 2610.03292

Geometrically distinct unbounded continua of solutions for Yamabe-type equations

Piotr Stefaniak
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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.

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Piotr Stefaniak. 2026-10-02. Geometrically distinct unbounded continua of solutions for Yamabe-type equations. https://arxiv.org/abs/2610.03292

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