The Obata equation with Robin boundary condition

Xuezhang Chen ^[1] ; Mijia Lai ^[2] ; Fang Wang ^[2]
1. [1] Nanjing University
  
  Nanjing University
  
  China
2. [2] Shanghai Jiao Tong University
  
  Shanghai Jiao Tong University
  
  China
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 2, 2021, págs. 643-670
Idioma: inglés
DOI: 10.4171/rmi/1212
Enlaces
- Texto completo
Resumen
- 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.