Regularity theory for the generalized Neumann problem for Yang-Mills connections -- non-trivial examples in dimensions 3 and 4 (Q1568223)

The author gives existence and regularity results for a generalized Neumann problem on Yang-Mills connection. Let \(M\) be a Riemannian manifold of dimension 3 or 4 with smooth boundary. Let \(P\) be a \(\text{SU}(N)\)-principal bundle over \(M\), endowed with an involution \(\varphi\) on \(\partial M\), where the involution \(\varphi\) is a smooth map from \(\partial M\) into \(\{s \in \text{SU}(N)\); \(s^2 = 1\}\). Such involutions are induced by reflections on \(\partial M\) when we double the manifold \(M\). Then the author proves that there exists a smooth solution for a generalized Neumann problem compatible with the involution \(\varphi\). She also gives conditions under which the solutions are non-trivial.