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 inequali...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.展开更多
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)。
文摘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.
