| Abstract | We study the Nehari manifold N associated to the boundary value problem −Δ u = f(u) , u ın H_0^1 (Ømega ), where Ømega is a bounded regular domain in R^n. Using elementary tools from Differential Geometry, we provide a local description of \N as an hypersurface of the Sobolev space H^1_0 (Ømega ). We prove that, at any point u ın \N, there exists an exterior tangent sphere whose curvature is the limit of the increasing sequence of principal curvatures of \N. Also, the H_1-norm of u ın \N depends on the number of principal negative curvatures. Finally, we study basic properties of an angle decreasing flow on the Nehari manifold associated to homogeneous non–linearities. |
