A regularity result for the bound states of N-body Schrödinger operators: Blow-ups and Lie manifolds

Abstract: I will present a result on the regularity of the eigenfunctions of the usual $N$-body Hamiltonian. The proof is in two steps: Firstly, we built a compactification of $R^{3N}$ that is compatible with the analytic properties of the $N$-body Hamiltonian. To build this space, we blow-up $R^{3N}$ by the spheres at infinity of the collision planes (at this level, the resulting space is the Georgescu-Vasy compactification) then we blow-up again by the collision planes. Secondly, we meticulously study how the Lie manifold structure of $R^{3N}$ and the associated data (metric, Sobolev spaces, differential operators) change with each blow-up. This is a joint work with B. Ammann and V. Nistor.

analysis of PDEsdifferential geometryspectral theory

Audience: researchers in the topic

Oldenburg analysis seminar