6 problems

Let four bodies with positive masses be arranged in a specified ordering along the boundary of their convex hull. A planar configuration is convex if no body lies inside or on the…

A convex configuration of four bodies has no body inside or on the convex hull formed by the other three bodies. A central configuration is one in which the acceleration vector of…

Let $f$ be the function whose critical points represent central configurations in the four-body problem, and let $\mathcal{C}_4$ be the quotient configuration space with Poincaré p…

Consider the planar four-body problem with homogeneous potential exponent $A$, and compare its central configurations with those in the Newtonian case $A=3$. Albouy's conjecture. F…

Isosceles trapezoid subconjecture. There exists a unique convex central configuration having two pairs of equal masses located at the adjacent vertices of the configuration, and it…

Albouy–Fu's convex conjecture. For the planar four-body problem, there is a unique convex central configuration for each ordering of the masses on the boundary of its convex hull.