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.
Bellettini, G., Novaga, M. (1999). A result on motion by mean curvature in arbitrary codimension. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 11(3), 205-220 [10.1016/S0926-2245(99)00030-3].
A result on motion by mean curvature in arbitrary codimension
BELLETTINI, GIOVANNI;
1999-01-01
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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https://hdl.handle.net/11365/1017412