Smooth compactness of self-shrinkers

Original manuscript July 15, 2009We prove a smooth compactness theorem for the space of embedded self-shrinkers in R[superscript 3]. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow.National Science Foundation (U.S.) (Grant DMS 0606629)National Science Foundation (U.S.) (Grant DMS 0405695