Spacelike Self-Similar Solutions of the Mean Curvature Flow
Márcio Rostirolla Adames
Broschiertes Buch

Spacelike Self-Similar Solutions of the Mean Curvature Flow

in Pseudo-Euclidean Spaces

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The Mean Curvature Flow is, maybe, the most natural way to deform an immersed submanifold; it deforms an immersion into something "rounder" or "more regular". The Mean Curvature Flow is a much studied tool and one of its problems is that it also produces singularities. These singularities are related to some kinds of self-similar solutions of the MCF. A very important class of self-similar solutions is formed by the self-shrinkers. These are homotheties generated by the MCF which shrink the initial immersion. There are several works about singularity formation for the MCF in Euclidean Space (s...