The Obata equation with Robin boundary condition
Copyright policy )The Obata equation with Robin boundary condition
We study the Obata equation with Robin boundary condition \partial f/\partial \nu + 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 \partial f/\partial \nu=1 .
- Nanjing University China (People's Republic of)
- Shanghai Jiao Tong University China (People's Republic of)
- Nanjing University China (People's Republic of)
Mathematics - Differential Geometry, Obata equation, Differential Geometry (math.DG), Spectral problems; spectral geometry; scattering theory on manifolds, FOS: Mathematics, Rigidity results, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Robin boundary condition, 53C25
Mathematics - Differential Geometry, Obata equation, Differential Geometry (math.DG), Spectral problems; spectral geometry; scattering theory on manifolds, FOS: Mathematics, Rigidity results, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Robin boundary condition, 53C25
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