Submitted Paper

Inserted: 12 jun 2026
Last Updated: 12 jun 2026

Year: 2026

Abstract:

We prove rigidity and classification results for the quasilinear Liouville equation associated with the $n$-Laplacian on complete noncompact Riemannian manifolds with nonnegative Ricci curvature. Our first result shows that, under a sharp logarithmic lower bound, the ambient manifold must be isometric to the Euclidean space and the solution must be one of the standard bubbles. We also prove a finite-mass rigidity theorem under the corresponding sharp asymptotic lower bound. We show that any logarithmic lower bound forces positive asymptotic volume ratio and one-endedness of the manifold. Finally, we construct solutions on nonflat manifolds with nonnegative Ricci curvature showing the sharpness of our hypotheses.

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