Lifespan theorem for constrained surface diffusion flows

Abstract

We consider closed immersed hypersurfaces in ${\mathbb{R}}^3$ and ${\mathbb{R}}^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.

29 pages. arXiv admin note: substantial text overlap with arXiv:1201.6574

Cited by in corpus (7)

• Surface diffusion flow near spheres
• The volume-preserving Willmore flow
• On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow
• Length-constrained curve diffusion
• The Willmore flow with prescribed isoperimetric ratio
• On the flow of non-axisymmetric perturbations of cylinders via surface diffusion
• Willmore Flow of Complete Surfaces