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    Article

    A rigidity theorem for ideal surfaces with flat boundary

    We consider surfaces with boundary satisfying a sixth-order nonlinear elliptic partial differential equation corresponding to extremising the \(L^2\)L2-norm of the gradient of the mean curvature. We show that suc...

    James McCoy, Glen Wheeler in Annals of Global Analysis and Geometry (2020)

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    Article

    Contracting convex hypersurfaces by curvature

    We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain smooth and uniformly convex, ...

    Ben Andrews, James McCoy, Yu Zheng in Calculus of Variations and Partial Differe… (2013)