Noncollision Singularities in a Planar Four-body Problem
Jinxin Xue

In this work (ArXiv: 1409.0048), we show that there is a Cantor set of
initial conditions in a planar four-body problem such that all four bodies
escape to infinity in finite time, avoiding collisions. This proves the
Painlevé conjecture for the four-body case, and thus settles the
conjecture completely. This work is a continuation of the work ArXiv:
1307.2645 jointly with D. Dolgopyat.