Formal asymptotics for blowup in the Willmore flow - Eurandom
Formal asymptotics for blowup in the Willmore flow - Eurandom
Formal asymptotics for blowup in the Willmore flow - Eurandom
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Introduction<br />
Consider an elastic surface. The elastic energy of <strong>the</strong> surface is<br />
given by<br />
<br />
E = (α + βH 2 + γK)dµ,<br />
where <strong>the</strong> <strong>in</strong>tegral is over <strong>the</strong> surface Ω and<br />
◮ H is <strong>the</strong> mean curvature,<br />
◮ K is <strong>the</strong> Gaussian curvature.<br />
The first term represents surface tension, while<br />
<strong>the</strong> second and third term model <strong>the</strong> bend<strong>in</strong>g<br />
energy. The equilibrium shape of certa<strong>in</strong> cells<br />
can be found by m<strong>in</strong>imis<strong>in</strong>g <strong>the</strong> bend<strong>in</strong>g energy.<br />
For example <strong>the</strong> red blood cell.<br />
Ω