Spacelike SelfSimilar Solutions of the Mean Curvature Flow: in PseudoEuclidean Spaces,Used

Spacelike SelfSimilar Solutions of the Mean Curvature Flow: in PseudoEuclidean Spaces,Used

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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 selfsimilar solutions of the MCF. A very important class of selfsimilar solutions is formed by the selfshrinkers. 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 (specially in lower dimension and codimension 1) and special interest into classifying these selfshrinkers because of their relation to the singularities of the MCF. In this book the autor studies the selfshrinkers of the MCF with higher codimension in PseudoEuclidean space. The results in this book generalize results of Smoczyk and Huisken, beyond this the nonexistence of such selfshrinkers is proven in several cases.

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