Weak asymptotical stability of Yang-Mills' gradient flow
The authors study the Yang-Mills functional \(J(\nabla)\) which is given by the square integral of the curvature associated to a metric connection \(\nabla\) on a Riemannian vector bundle E over a Riemannian manifold M. For the case where M is the Euclidean space \(R^ n\) or a bounded domain in \(R^ n\) with smooth boundary \((n\geq 2)\) and E is the trivial vector bundle they prove the asymptotical stability of the canonical flat connection of E (a critical point of the Yang-Mills functional) in certain function space for the gradient flow \(\nabla(t)\) satisfying the equation \(\frac{d\nabla(t)}{dt}=-\text{grad} J(\nabla(t))\). Special gauge conditions are assumed.
scientific article; zbMATH DE number 4131317