@article {Kuwert2014,
	title = {Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds},
	journal = {Mathematische Annalen},
	volume = {359},
	number = {1},
	year = {2014},
	month = {Jun},
	pages = {379{\textendash}425},
	abstract = {<p>We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})\&gt;6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.</p>},
	issn = {1432-1807},
	doi = {10.1007/s00208-013-1005-3},
	url = {https://doi.org/10.1007/s00208-013-1005-3},
	author = {Kuwert, Ernst and Andrea Mondino and Johannes Schygulla}
}
