Departmental Colloquium

A theorem of da Luz and Maderna asserts that the Newtonian N-body problem in $R^d$ admits no free-time action minimizers defined on the entire real line. In this talk we will see how, for $d \ge 3$, their result can be deduced from an extension of the Cheeger–Gromoll splitting theorem. This new proof allows us to generalize the result to a wider class of interaction potentials, which need not be homogeneous and may differ from one pair of bodies to another; the key property is subharmonicity. Joint work with Marco Mazzucchelli.