  We present a deterministic fully dynamic algorithm with subpolynomial
worst-case time per graph update such that after processing each update of the
graph, the algorithm outputs a minimum cut of the graph if the graph has a cut
of size at most $c$ for some $c = (\log n)^{o(1)}$. Previously, the best update
time was $\widetilde O(\sqrt{n})$ for any $c > 2$ and $c = O(\log n)$ [Thorup,
Combinatorica'07].
