Eigenvalues for the Clamped Plate Problem of L_(ν)^(2) Operator on Complete Riemannian Manifolds  

作　　者：Ling Zhong ZENG 

机构地区：[1]Jiangxi Provincial Center for Applied Mathematics&School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第9期2223-2243,共21页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.11861036 and 11826213);the Natural Science Foundation of Jiangxi Province(Grant No.20224BAB201002)。

摘　　要：L_(ν) operator is an important extrinsic differential operator of divergence type and has profound geometric settings.In this paper,we consider the clamped plate problem of L_(ν)^(2)operator on a bounded domain of the complete Riemannian manifolds.A general formula of eigenvalues of L_(ν)^(2) operator is established.Applying this general formula,we obtain some estimates for the eigenvalues with higher order on the complete Riemannian manifolds.As several fascinating applications,we discuss this eigenvalue problem on the complete translating solitons,minimal submanifolds on the Euclidean space,submanifolds on the unit sphere and projective spaces.In particular,we get a universal inequality with respect to the L_(II) operator on the translating solitons.Usually,it is very difficult to get universal inequalities for weighted Laplacian and even Laplacian on the complete Riemannian manifolds.Therefore,this work can be viewed as a new contribution to universal estimate.

关 键 词：Mean curvature flows L_(ν)^(2)operator clamped plate problem EIGENVALUES Riemannian manifolds translating solitons 

分 类 号：O186.12[理学—数学]