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
Properties of Willmore flow ◮ The Willmore flow is a fourth order, nonlinear, differential equation. ◮ Short time existence (parabolic quasi linear) ◮ Long time existence ◮ for solutions close to a local minimum ◮ for immersed spheres with Willmore energy lower equal to 8π ◮ two-dimensional graphs ◮ If blowup occurs, the blowup profile must be stationary.
Problem Can the Willmore flow create a singularity on a smooth surface in finite time?
- Page 1 and 2: Formal asymptotics for blowup in th
- Page 3 and 4: Introduction Consider an elastic su
- Page 5 and 6: The Willmore flow I Since the integ
- Page 7 and 8: The Willmore flow II The Willmore f
- Page 9 and 10: The sphere Consider a sphere of rad
- Page 11: The sphere and more ◮ The Willmor
- Page 15 and 16: Numerical computations Numerical co
- Page 17 and 18: Matched asymptotics On every region
- Page 19 and 20: Results ◮ Matching gives (T − t
Properties of <strong>Willmore</strong> <strong>flow</strong><br />
◮ The <strong>Willmore</strong> <strong>flow</strong> is a fourth order, nonl<strong>in</strong>ear, differential<br />
equation.<br />
◮ Short time existence (parabolic quasi l<strong>in</strong>ear)<br />
◮ Long time existence<br />
◮ <strong>for</strong> solutions close to a local m<strong>in</strong>imum<br />
◮ <strong>for</strong> immersed spheres with <strong>Willmore</strong> energy lower equal to 8π<br />
◮ two-dimensional graphs<br />
◮ If <strong>blowup</strong> occurs, <strong>the</strong> <strong>blowup</strong> profile must be stationary.
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