Entropy and codimension bounds for generic singularities

arXiv1906.07609MaRDI QIDQ6320689

William P. II. Minicozzi, Tobias Holck Colding

Publication date: 18 June 2019

Abstract: We show that all closed $2$-dimensional singularities for higher codimension mean curvature flow that cannot be perturbed away have uniform entropy bounds and lie in a linear subspace of small dimension. The entropy and dimension of the subspace are both $leqC,(1+gamma)$ for some universal constant $C$ and genus $gamma$. These are the first general bounds on generic singularities in arbitrary codimension.

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