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- W1648609843 abstract "For two-dimensional, immersed closed surfaces $f:Sigma to R^n$, we study the curvature functionals $mathcal{E}^p(f)$ and $mathcal{W}^p(f)$ with integrands $(1+|A|^2)^{p/2}$ and $(1+|H|^2)^{p/2}$, respectively. Here $A$ is the second fundamental form, $H$ is the mean curvature and we assume $p > 2$. Our main result asserts that $W^{2,p}$ critical points are smooth in both cases. We also prove a compactness theorem for $mathcal{W}^p$-bounded sequences. In the case of $mathcal{E}^p$ this is just Langer's theorem cite{langer85}, while for $mathcal{W}^p$ we have to impose a bound for the Willmore energy strictly below $8pi$ as an additional condition. Finally, we establish versions of the Palais-Smale condition for both functionals." @default.
- W1648609843 created "2016-06-24" @default.
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- W1648609843 date "2011-08-30" @default.
- W1648609843 modified "2023-10-16" @default.
- W1648609843 title "Two-dimensional curvature functionals with superquadratic growth" @default.
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- W1648609843 doi "https://doi.org/10.48550/arxiv.1108.5855" @default.
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