摘要
In this paper,we compare the first order fractional GJMS(see Graham et al.(1992))operator P_(1) with the conformal Laplacian P_(2) on the conformal infinity of a Poincaré-Einstein manifold.We derive some inequalities between the Yamabe constants and the first eigenvalues associated with P_(1) and P_(2),and prove some rigidity theorems by characterizing the equalities.Similarly,some comparison theorems between P_(2) and the Paneitz operator P_(4) or the 6 th order GJMS operator P_(6) are also given.
基金
supported by National Natural Science Foundation of China(Grant Nos.11871331 and 11571233)
supported by National Natural Science Foundation of China(Grant No.11871331)。
