Resumen de The Obata equation with Robin boundary condition

Xuezhang Chen, Mijia Lai, Fang Wang

• We study the Obata equation with Robin boundary condition ∂f/∂ν+af=0 on manifolds with boundary, where a is a non-zero constant. Dirichlet and Neumann boundary conditions were previously studied by Reilly, Escobar and Xia. Compared with their results, the sign of a plays an important role here. The new discovery shows besides spherical domains, there are other manifolds for both a>0 and a<0. We also consider the Obata equation with non-vanishing Neumann condition ∂f/∂ν=1.