On the geometric dependence of Riemannian Sobolev best constants
Abstract
We concerns here with the continuity on the geometry of the second Riemannian Lp-Sobolev best constant B0(p,g) associated to the AB program. Precisely, for 1 <= p <= 2, we prove that B0(p,g) depends continuously on g in the C2-topology. Moreover, this topology is sharp for p = 2. From this discussion, we deduce some existence and C0-compactness results on extremal functions.
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