  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.
