Vincent Edward Moncrief is an American mathematician and physicist at Yale University.

A key result (obtained jointly with Arthur Fischer of the University of California at Santa Cruz) was to relate the reduced Hamiltonian for Einstein's equations to a topological invariant known as the Yamabe invariant (or sigma constant) for the spatial manifold and to show that the reduced Hamiltonian is monotonically decreasing along all solutions of the field equations (in the direction of cosmological expansion) and therefore evidently seeking to attain its infimum which in turn is expressible in terms of the sigma constant.

A discussion of this and related work (with Lars Andersson of the University of Miami and Yvonne Choquet-Bruhat of the Université Paris VI) may be found in Moncrief's and Choquet-Bruhat's lectures at the Cargese summer school on 50 years of the Cauchy Problem in General Relativity.

He is also interested in how a study of the "Einstein flow" on various manifolds might shed light on open questions in 3-manifold topology itself.

Most of this research involves the treatment of sufficiently small but nevertheless fully non-linear perturbations of certain special backgrounds and includes an analysis of higher as well as lower-dimensional spacetimes in addition to physical (3 + 1)-dimensional spacetime.