Uhlenbeck's compactness theorem

In differential geometry and in particular Yang–Mills theory, Uhlenbeck's compactness theorem is a result about sequences of (weak Yang–Mills) connections with uniformly bounded curvature having weakly or uniformly convergent subsequences up to gauge. It is an important theorem used in the compactification of the anti self-dual Yang–Mills moduli space (ASDYM moduli space), which is central to the construction of Donaldson invariants on four-dimensional manifolds (short 4-manifold) or monopole Floer homology on three-dimensional manifolds (short 3-manifold). The theorem is named after Karen Uhlenbeck, who first described it in 1982. In 2019, Uhlenbeck became the first woman to be awarded the Abel Prize, in part for her contributions to partial differential equations and gauge theory. Uhlenbeck's compactness theorem was generalized to Yang–Mills flows by Alex Waldron in 2018.