The paper entitled "Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature" by T Ilmanen constructs Brakke's motion from Allen-Cahn equation, which is one of the measure theoretic approaches to motion by mean curvature.This book first proposes a new idea that involves a new equation of the Allen-Cahn type to construct Brakke's motion; secondly explaining how to construct it through Ilmanen's approach as easily as possible.
