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- W2809822320 abstract "This work investigates the formation of singularities under the steepest descent $L^2$-gradient flow of the functional $mathcal W_{lambda_1, lambda_2}$, the sum of the Willmore energy, $lambda_1$ times the area, and $lambda_2$ times the signed volume of an immersed closed surface without boundary in $mathbb R^3$. We show that in the case that $lambda_1>1$ and $lambda_2=0$ any immersion develops singularities in finite time under this flow. If $lambda_1 >0$ and $lambda_2 > 0$, embedded closed surfaces with energy less than $$8pi+min{(16 pi lambda_1^3)/(3lambda_2^2), 8pi}$$ and positive volume evolve singularities in finite time. If in this case the initial surface is a topological sphere and the initial energy is less than $8 pi$, the flow shrinks to a round point in finite time. We furthermore discuss similar results for the case that $lambda_2$ is negative." @default.
- W2809822320 created "2018-07-10" @default.
- W2809822320 creator A5062414279 @default.
- W2809822320 date "2018-07-05" @default.
- W2809822320 modified "2023-09-27" @default.
- W2809822320 title "A note on singularities in finite time for the constrained Willmore flow" @default.
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