%0 Journal Article
%T Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds
%A Ernst Kuwert
%A Andrea Mondino
%A Johannes Schygulla
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s00208-013-1005-3
%X We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold M. Under the assumption that the sectional curvature of M is strictly positive, we prove the existence of a smoothly immersed sphere minimizing the L^{2} integral of the second fundamental form. Assuming instead that the sectional curvature is less than or equal to 2, and that there exists a point in M with scalar curvature bigger than 6, we obtain a smooth 2-sphere minimizing the integral of 1/4|H|^{2} +1, where H is the mean curvature vector.
%U http://arxiv.org/abs/1111.4893v1