This research shows uniqueness results for compact Riemannian manifolds, indicating Sobolev inequalities apply broadly.
We study some Sobolev trace inequalities on Riemannian manifolds with boundary. Using an adequate Bochner-Reilly type formula, we obtain some uniqueness result for compact n {n} -dimensional Riemannian manifolds of non-negative Ricci curvature and strictly convex boundary, where 2 ≤ n ≤ 9 2≤ n≤ 9 . As an application of this result, we derive Sobolev and logarithmic trace inequalities with explicit constants.
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Abdolhakim Shouman (2026) studied this question.
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