On the compactness problem of extremal functions to sharp Riemannian Lp-Sobolev inequalities

Let (M,g) be a smooth compact Riemannian manifold without boundary of dimension n⩾2. For 10. The continuity of the map p∈[1,q0)↦B0(p,g) is discussed in detail since it plays a key role in the proof of the main theorem.