192 citations
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4 papers · 1 filter
Global analysis of the generalised Helfrich flow of closed curves immersed in
Glen Wheeler
In this paper we consider the evolution of regular closed elastic curves immersed in . Equipping the ambient Euclidean space with a vector field $\ca:\R^n\rightarrow\R^n$…
Lifespan theorem for constrained surface diffusion flows
James McCoy, Glen Wheeler, Graham Williams
We consider closed immersed hypersurfaces in and evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore…
Surface diffusion flow near spheres
Glen Wheeler
We consider closed immersed hypersurfaces evolving by surface diffusion flow, and perform an analysis based on local and global integral estimates. First we show that a properly im…
Convex hypersurfaces with pinched principal curvatures and flow of convex hypersurfaces by high powers of curvature
Ben Andrews, James McCoy
We consider convex hypersurfaces for which the ratio of principal curvatures at each point is bounded by a function of the maximum principal curvature with limit 1 at infinity. We…