Formal asymptotics for blowup in the Willmore flow - Eurandom

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$Continuous-time random walks, fractional calculus and ... - Eurandom$

Surface evolution Consider a moving surface φ(t) : M → R 3 parametrised by t, with metric gij = 〈∂iφ, ∂jφ〉. ¯φt(p, t) p q ¯φt(q, t) Here, ¯ φt is the displacement of the surface in the normal direction.
The Willmore flow II The Willmore flow is given by with ◮ H : mean curvature, ◮ K : Gaussian curvature, ¯φt = −∆H − 2H(H 2 − K), ◮ ∆ : Laplace-Beltrami operator. Generalisation of Laplacian given by 1 ∆ = √ ∂i g det g ij det g∂j .
Page 1 and 2: Formal asymptotics for blowup in th
Page 3 and 4: Introduction Consider an elastic su
Page 5: The Willmore flow I Since the integ
Page 9 and 10: The sphere Consider a sphere of rad
Page 11 and 12: The sphere and more ◮ The Willmor
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

Formal asymptotics for blowup in the Willmore flow - Eurandom

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