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
The sphere and more ◮ The Willmore energy for a sphere is 4π. ◮ The Willmore energy is scale invariant. ◮ The sphere is a global minimum for closed immersed surfaces.
The sphere and more ◮ The Willmore energy for a sphere is 4π. ◮ The Willmore energy is scale invariant. ◮ The sphere is a global minimum for closed immersed surfaces. A surface with κ1 = −κ2, everywhere, is also a stationary solution (H = 0). This surface is given by the graph z r(z) = q cosh , q rotated around the z-axis.
- 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: The sphere Consider a sphere of rad
- Page 13 and 14: Problem Can the Willmore flow creat
- 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
The sphere and more<br />
◮ The <strong>Willmore</strong> energy <strong>for</strong> a sphere is 4π.<br />
◮ The <strong>Willmore</strong> energy is scale <strong>in</strong>variant.<br />
◮ The sphere is a global m<strong>in</strong>imum <strong>for</strong> closed immersed surfaces.
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