Aubin's lemma for the Yamabe constants of infinite coverings and a positive mass theorem
A generalization of Aubin's lemma for the Yamabe constant of infinite conformal coverings \((M_\infty ,C_\infty)\) of a closed positive conformal manifold \((M,C)\) is proved, under the condition that \(\pi_1(M)\) has a descending chain of finite index subgroups tending to \(\pi_1(M_\infty)\). A version of positive mass theorem for a specific class of asymptotically flat manifolds with singularities is established. This is used to prove that if the covering \(M_\infty\) is normal, then the limit of the Yamabe constants of the finite conformal coverings associated to the descending chain is equal to that of \((M_\infty ,C_\infty)\).
scientific article; zbMATH DE number 6021950
scientific article