Reverse bubbling of currents and harmonic heat flows with prescribed singular set (Q1879422)

This paper is largely based on the author's PhD thesis. The author considers the harmonic heat flow for maps \(u\) between \(B^3\), the unit ball of \(\mathbb{R}^3\), and its boundary \(S^2\). For a class of possibly singular initial and boundary data he shows the existence of a weak solution whose singular set is a fixed discrete set on the vertical axis arbitrarily prescribed. Other examples including isolated singularities moving along a prescribed trajectory are also given.