Spectrum and involutions
Alessandro Savo Università di Roma
This is a joint work with Bruno Colbois. Consider a compact Riemannian manifold with an involutive isometry , and assume that the distance of any point to its image under is bounded below by a positive constant (the smallest displacement). We observe that this simple geometric situation has a strong consequences on the spectrum of a large class of -invariant operators (including the Schrödinger operator acting on functions and the Hodge Laplacian acting on forms): roughly speaking, the gap between the first and the second eigenvalue of is uniformly bounded above by a constant depending only on the displacement (in particular, not depending on ).