Two-dimensional curvature functionals with superquadratic growth

Ernst Kuwert, Tobias Lamm, Yuxiang Li

For two-dimensional, immersed closed surfaces $f:\Sigma \to {\mathbb{R}}^n$, we study the curvature functionals ${\mathcal{E}}^p(f)$ and ${\mathcal{W}}^p(f)$ with integrands $(1+|A{|}^2{)}^{p/2}$ and $(1+…