Motion of Level Sets by Mean Curvature. I
نویسندگان
چکیده
We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature. This weak solution allows us then to define for any compact set Γo a unique generalized motion by mean curvature, existing for all time. We investigate the various geometric properties and pathologies of this evolution.
منابع مشابه
Motion of Level Sets by Mean Curvature. Ii
We give a new proof of short time existence for the classical motion by mean curvature of a smooth hypersurface. Our method consists in studying a fully nonlinear uniformly parabolic equation satisfied by the signed distance function to the surface
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