Martedì 13 Gennaio 2026, alle ore 15:30 in Aula U1-03 (Piano -1 | Edificio U1 | Piazza della Scienza 1, Milano), il Prof. Carlo Morpurgo (University of Missouri) terrà il seguente intervento
Titolo: Sharp Sobolev inequalities on noncompact Riemannian manifolds with bounded Ricci curvature
Abstract: Given a smooth, complete, Riemannian manifold (M, g), the Sobolev embedding W1,p(M) → Lq(M), when valid, can be expressed via an inequality of type
∥u∥αq ≤ A∥∇u∥αp + B∥u∥αp, 1 ≤ p < n, q = np / n – p , α > 0. (1)
The validity of (1), and the optimality of the constants A, B, have been widely studied in the late 1990s-early 2000s, notably by the schools of T. Aubin and E. Hebey, the creator of the celebrated “AB-program”. In this seminar, I will focus on the “A part” of this program, in particular about the validity of (1) when A = K(n,p)α, where K(n, p) is the sharp constant in the well-known inequality when M = Rn, with its standard metric. I will present some new results for noncompact manifolds subject minimal curvature restrictions. (Joint work with S. Nardulli and L. Qin)
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