Published Paper

Inserted: 7 mar 2022
Last Updated: 12 feb 2026

Journal: J. Eur. Math. Soc.
Volume: 28
Number: 1
Pages: 359-392
Year: 2026

Abstract:

In this paper we prove classification results for solutions to subcritical and critical semilinear elliptic equations with a nonnegative potential on noncompact manifolds with nonnegative Ricci curvature. We show in the subcritical case that all nonnegative solutions vanish identically. Moreover, under some natural assumptions, in the critical case we prove a strong rigidity result, namely we classify all nontrivial solutions showing that they exist only if the potential is constant and the manifold is isometric to the Euclidean space.

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• semilinear-kappa.pdf