  The long-time existence and umbilicity estimates for compact, graphical
solutions to expanding curvature flows are deduced in Riemannian warped
products of a real interval with a compact fibre. Notably we do not assume the
ambient manifold to be rotationally symmetric, nor the radial curvature to
converge, nor a lower bound on the ambient sectional curvature. The inverse
speeds are given by powers $p\leq 1$ of a curvature function satisfying few
common properties.
