Mean curvature flow and related flows are important tools in mathematics and mathematical physics. For example, the famous Penrose conjecture in general relativity by Huisken and Ilmanan was based on a curvature flow approach. Under mean curvature flow, surfaces usually develop singularities in finite time. This book presents techniques in the study of singularities of mean curvature flow. It details the influential work of K. Brakke as well as such recent developments as relations to regularity theory for minimal surfaces, as in Allard's and de Giorgi's work.
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Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.
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