We prove a conjecture formulated by De Giorgi concerning the connections between motion by mean curvature of a k-dimensional submanifold without boundary in R-n and the evolution of its tubular neighbourhoods by the sum of the k smallest curvatures. The result holds also after the onset of singularities.
A result on motion by mean curvature in arbitrary codimension
NOVAGA, MATTEO
1999
Abstract
We prove a conjecture formulated by De Giorgi concerning the connections between motion by mean curvature of a k-dimensional submanifold without boundary in R-n and the evolution of its tubular neighbourhoods by the sum of the k smallest curvatures. The result holds also after the onset of singularities.
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