Ricerc@Sapienza

Let Ω be a compact Riemannian manifold with smooth boundary and let utbe the solution of the heat equation on Ω , having constant unit initial data u0= 1 and Dirichlet boundary conditions (ut= 0 on the boundary, at all times). If at every time t the normal derivative of utis a constant function on the boundary, we say that Ω has the constant flow property. This gives rise to an overdetermined parabolic problem, and our aim is to classify the manifolds having this property.