Nonuniqueness for the Yang–Mills heat flow

Abstract

We prove nonuniqueness for the Yang–Mills heat flow on bundles over manifolds of dimension m⩾5. For 5⩽ m⩽9 and any n∈ N there is an initial connection on the trivial bundle R m× SO(m) which, when evolved by the Yang–Mills heat flow, develops a point singularity in finite time, such that there are at least n different smooth continuations after the singular time. Moreover, the solution to the Yang–Mills heat flow may continue on a different bundle after the singular time, and for m∈{6,8} not even the topology of the bundle is determined uniquely.