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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 surfacedoi:10.1090/s0002-9947-1992-1068927-8 fatcat:6h3eyv3yzbgudkfs5qu7lmakrm