%0 Journal Article
%T Immersed Spheres of Finite Total Curvature into Manifolds
%A Andrea Mondino
%A Tristan Rivi¨¨re
%J Mathematics
%D 2013
%I arXiv
%R 10.1515/acv-2013-0106
%X We prove that a sequence of possibly branched, weak immersions of the two-sphere $S^2$ into an arbitrary compact riemannian manifold $(M^m,h)$ with uniformly bounded area and uniformly bounded $L^2-$norm of the second fundamental form either collapse to a point or weakly converges as current, modulo extraction of a subsequence, to a Lipschitz mapping of $S^2$ and whose image is made of a connected union of finitely many, possibly branched, weak immersions of $S^2$ with finite total curvature. We prove moreover that if the sequence belongs to a class $\gamma$ of $\pi_2(M^m)$ the limiting lipschitz mapping of $S^2$ realizes this class as well.
%U http://arxiv.org/abs/1305.6205v1