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
In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study ...In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.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.
基金supported by NSF grant DMS-1509505a postdoctoral fellowship of the National Science Foundation(No.DMS-1103786)
文摘In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.
