TY - JOUR
T1 - A Note on Obata Equations on Manifolds with Boundary
AU - Lai , Mijia
AU - Zhou , Huihuang
JO - Journal of Mathematical Study
VL - 3
SP - 242
EP - 253
PY - 2022
DA - 2022/09
SN - 55
DO - http://doi.org/10.4208/jms.v55n3.22.02
UR - https://global-sci.org/intro/article_detail/jms/20974.html
KW - Obata type equation, manifolds with boundary, Dupin hypersurfaces.
AB - <p style="text-align: justify;">We analyze complete manifolds with boundary which admit solutions to Obata type equations $\nabla^2 f- fg=0$ and $\nabla^2 f=g$ under various boundary conditions. Given the existence of interior critical points, such manifolds are domains in the hyperbolic space and the Euclidean space respectively.</p>