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Lifespan theorem for constrained surface diffusion flows
Faculty of Informatics - Papers (Archive)
  • James McCoy, University of Wollongong
  • Glen Wheeler, University of Wollongong
  • Graham Williams, University of Wollongong
Publication Date
Publication Details

McCoy, J., Wheeler, G. & Williams, G. (2011). Lifespan theorem for constrained surface diffusion flows. Mathematische Zeitschrift, 269 (1-2), 147-178.

We consider closed immersed hypersurfaces in R^3 and 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 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.
Citation Information
James McCoy, Glen Wheeler and Graham Williams. "Lifespan theorem for constrained surface diffusion flows" (2011) p. 147 - 178
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