Tensorial version of the calculus of variations.
The Approximation of Instantons.
The configuration space of gauge theory on open manifolds of bounded geometry
We define suitable Sobolev topologies on the space of connections of bounded geometry and finite Yang-Mills action and the gauge group and show that the corresponding configuration space is a stratified space. The underlying open manifold is assumed to have bounded geometry.
The existence of gaps in minimal foliations.
The Gluck and Ziller problem with the euclidean metric
The gradient flow of Higgs pairs
We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle over a Kähler surface , and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point of this functional. We also prove that the limiting Higgs pair can be extended smoothly to a vector bundle over...
The information metric on rational maps.
The Lagrange complex
The singularities of Yang-Mills connections for bundles on a surface.
The singularities of Yang-Mills connections for bundles on a surface.
The singularity structureοf the Yang-Mills configuration space
The geometric description of Yang–Mills theories and their configuration space is reviewed. The presence of singularities in M is explained and some of their properties are described. The singularity structure is analysed in detail for structure group SU(2). This review is based on [28].
The Smith Conjecture in dimension four and equivariant gauge theory.