Motion of level sets by mean curvature IV |
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Authors: | Lawrence C Evans Joel Spruck |
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Institution: | 1. Department of Mathematics, University of California, 94720, Berkeley, CA 2. Department of Mathematics, University of Massachusetts, 01003, Amherst, MA
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Abstract: | We continue our investigation of the “level-set” technique for describing the generalized evolution of hypersurfaces moving according to their mean curvature. The principal assertion of this paper is a kind of reconciliation with the geometric measure theoretic approach pioneered by K. Brakke: we prove that almost every level set of the solution to the mean curvature evolution PDE is in fact aunit-density varifold moving according to its mean curvature. In particular, a.e. level set is endowed with a kind of “geometric structure.” The proof utilizes compensated compactness methods to pass to limits in various geometric expressions. |
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