A Note on Obata Equations on Manifolds with Boundary  

作　　者：Mijia Lai Huihuang Zhou 

机构地区：[1]School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China [2]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

出　　处：《Journal of Mathematical Study》2022年第3期242-253,共12页数学研究（英文）

基　　金：supported in part by National Natural Science Foundation of China No.12031012,No.12171313;the Institute of Modern Analysis-A Frontier Research Center of Shanghai;supported in part by the Natural Science Foundation of China(Grant No.11871331);Shanghai Science and Technology Innovation Action Plan(Grant No.20JC1413100).

摘　　要：We analyze complete manifolds with boundary which admit solutions to Obata type equations▽^(2)f-fg=0 and▽^(2)f=g under various boundary condition-s.Given the existence of interior critical points,such manifolds are domains in the hyperbolic space and the Euclidean space respectively.

关 键 词：Obata type equation manifolds with boundary Dupin hyper surf aces 

分 类 号：O17[理学—数学]