Before revision:  As a consequence, we get fully-dynamic \varepsilon-coreset algorithms for k-median and k-means with worst-case update time O(\varepsilon^{-2}k^2\log^5 n \log^3 k) and coreset size O(\varepsilon^{-2}k\log n \log^2 k) ignoring \log \log n and \log(1/\varepsilon) factors and assuming that \varepsilon, \lambda = \Omega(1/poly(n)) (very weak assumptions made to make bounds easy to parse) .
After revision:  As a consequence, we get fully-dynamic \varepsilon-coreset algorithms for k-median and k-means with worst-case update time O(\varepsilon^{-2}k^2\log^5 n \log^3 k) and coreset size O(\varepsilon^{-2}k\log n \log^2 k) ignoring \log \log n and \log(1/\varepsilon) factors and assuming that \varepsilon, \lambda = \Omega(1/poly(n)) .