  We consider a closed Willmore surface properly immersed in ${\R}^m$ (m>2)
with square-integrable second fundamental form, and with one point-singularity
of finite arbitrary integer order. Using the "conservative" reformulation of
the Willmore equation introduced in a previous paper by the second author, we
show that, in an appropriate conformal parametrization, the gradient of the
Gauss map of the immersion has bounded mean oscillations if the singularity has
order one, and is bounded if the order is at least two. We develop around the
singular point local asymptotic expansions for the immersion, its first and
second derivatives, and for the mean curvature vector. Finally, we exhibit an
explicit condition ensuring the removability of the point-singularity

Analysis of PDEs;Differential Geometry