The Li-Yau-Hamilton estimate and the Yang-Mills heat equation on manifolds with boundary (Q960554)

The main goal of the very interesting paper under review is twofold. First of all, estimates are established in the spirit of Li-Yau-Hamilton for the heat equation over a manifold \(M\) with nonempty boundary, which are typically used to obtain monotonicity formulae related to geometric flows. Further on, with the aid of the Li-Yau-Hamilton estimate the author derives bounds for a solution \(\nabla (t)\) of the Yang-Mills heat equation in a vector bundle over \(M.\) In particular, the results imply that the curvature of \(\nabla (t)\) does not blow up if the dimension of \(M\) is less than \(4\) or if the initial energy of \(\nabla (t)\) is sufficiently small.