# A sharp Sobolev inequality on Riemannian manifolds by Li Y.Y., Ricciardi T.

By Li Y.Y., Ricciardi T.

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When n = 6 and r = r¯ = 3/2, we have: U 2∗ ,µ−1 α U r−1 U2 ∗ −2 1 2/3 ) µα ≤ Cµ−2 α ≤ C(log 2∗ ,µ−1 α 2∗ ,µ−1 α = U 2∗ ,µ−1 α ≤ C(log We know |Yg (ξxg˜α ,λα ) − K −2 | ≤ Cµ4α log 1 2/3 ) . µα 1 . 1 we have uα Lr¯ (Bα ) ≥ C −1 µ2α log 1 µα 2/3 . Inserting into (64), we obtain αµ4α log 1 µα 4/3 ≤ C µ4α log 1 µα 4/3 + αµ4α log 1 . µα Once again we obtain α ≤ C, a contradiction. 1 is thus established in the remaining limit case n = 6. 2. We adapt some ideas from [6]. Let (M, g) be a smooth compact Riemannian manifold without boundary, n ≥ 3.

Lieb, One-electron relativistic molecules with Coulomb interaction, Comm. Math. Phys. 90 (1983), 497–510. [16] W. Ding, J. Jost, J. Li and G. Wang, The differential equation ∆u = 8π − 8πeu on a compact Riemannian surface, Asian J. Math. 1 (1997), 230–248. [17] O. Druet, The best constants problem in Sobolev inequalities, Math. Ann. 314 (1999), 327–346. [18] O. Druet, Isoperimetric inequalities on compact manifolds, Geometria Dedicata, to appear. [19] O. Druet, E. Hebey and M. Vaugon, Sharp Sobolev inequalities with lower order remainder terms, Trans.

Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), 479–495. [37] R. -T. Yau, Lectures on Differential Geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, Volume I, International Press, Boston, 1994. 34 [38] G. Stampacchia, Le probl`eme de Dirichlet pour les ´equations elliptiques du second ordre ` a coefficients discontinus, Ann. Inst. Fourier, Grenoble 15 (1965), 189–258. [39] M. Struwe, Critical points of embeddings of H01,n into Orlicz spaces, Ann.