  We consider the $L^2$ gradient flow for the Willmore functional in Riemannian
manifolds of bounded geometry. In the euclidean case E.\;Kuwert and
R.\;Sch\"atzle [\textsl{Gradient flow for the Willmore functional,} Comm. Anal.
Geom., 10: 307-339, 2002] established a lower bound of a smooth solution of
such a flow, which depends only on how much the curvature of the initial
surface is concentrated in space. In a second joint work [\textsl{The Willmore
flow with small initial energy,} J.\;Differential Geom., 57: 409-441, 2001] the
aforementioned authors proved that a suitable blow-up converges to a nonumbilic
(compact or noncompact) Willmore surface. In the lecture notes of the first
author [\textsl{The Willmore Functional,} unpublished lecture notes, ETH
Z\"urich, 2007] the blow-up analysis was refined. In the present work we intend
to generalize the results mentioned above to the Riemannian setting.
