By Li Y.Y., Ricciardi T.
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Additional resources for A sharp Sobolev inequality on Riemannian manifolds
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 . Let (M, g) be a smooth compact Riemannian manifold without boundary, n ≥ 3.
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