“…A successful best constants theory on sharp potential type Riemannian Sobolev inequalities relies on answers to a number of questions related to the optimal constants A 0 (n, F, G, g) and B 0 (n, F, G, g) and to the sharp Sobolev inequalities (10) and (11). In the same spirit of the scalar AB program, we inquire: (A) Is it possible to find the explicit values and/or bounds for A 0 (n, F, G, g) and B 0 (n, F, G, g)?…”