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• W1569480955 abstract "In this paper we study the steepest descent $L^2$-gradient flow of the functional $SW_{lambda_1,lambda_2}$, which is the the sum of the Willmore energy, $lambda_1$-weighted surface area, and $lambda_2$-weighted enclosed volume, for surfaces immersed in $R^3$. This coincides with the Helfrich functional with zero `spontaneous curvature'. Our first results are a concentration-compactness alternative and interior estimates for the flow. For initial data with small energy, we prove preservation of embeddedness, and by directly estimating the Euler-Lagrange operator from below in $L^2$ we obtain that the maximal time of existence is finite. Combining this result with the analysis of a suitable blowup allows us to show that for such initial data the flow contracts to a round point in finite time." @default.
• W1569480955 created "2016-06-24" @default.
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• W1569480955 date "2012-01-22" @default.
• W1569480955 modified "2023-10-08" @default.
• W1569480955 title "Finite time singularities for the locally constrained Willmore flow of surfaces" @default.
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