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- W4293351153 abstract "We show that the concept of $H^2$-gradient flow for the Willmore energy and other functionals that depend at most quadratically on the second fundamental form is well-defined in the space of immersions of Sobolev class $W^{2,p}$ from a compact, $n$-dimensional manifold into Euclidean space, provided that $p geq 2$ and $p>n$. We also discuss why this is not true for Sobolev class $H^2=W^{2,2}$. In the case of equality constraints, we provide sufficient conditions for the existence of the projected $H^2$-gradient flow and demonstrate its usability for optimization with several numerical examples." @default.
- W4293351153 created "2022-08-27" @default.
- W4293351153 creator A5028635978 @default.
- W4293351153 date "2017-03-19" @default.
- W4293351153 modified "2023-09-27" @default.
- W4293351153 title "On $H^2$-gradient Flows for the Willmore Energy" @default.
- W4293351153 doi "https://doi.org/10.48550/arxiv.1703.06469" @default.
- W4293351153 hasPublicationYear "2017" @default.
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