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math.AP2026
Survey on topological methods for Allen--Cahn equations and systems
João Henrique Andrade, Stefano Nardulli, Raoní Ponciano
We present a survey on multiplicity results for the Allen--Cahn equation and systems in the singular perturbation regime, emphasizing their geometric interpretation through -con…
math.AP2026
Sharp Sobolev inequalities on noncompact Riemannian manifolds with bounded Ricci curvature
Carlo Morpurgo, Stefano Nardulli, Liuyu Qin
Given a smooth, complete Riemannian manifold with bounded Ricci curvature and positive injectivity radius, we derive a sharp Sobolev inequality for the embedding of $W^{1,p}(M)…