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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 />

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