Curvature decay estimates of graphical mean curvature flow in higher codimensions

Smoczyk, Knut; Tsui, Mao-Pei; Wang, Mu-Tao

doi:10.1090/tran/6624

Curvature decay estimates of graphical mean curvature flow in higher codimensions
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by Knut Smoczyk, Mao-Pei Tsui and Mu-Tao Wang PDF

Trans. Amer. Math. Soc. 368 (2016), 7763-7775 Request permission

Abstract:

We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions for a flat ambient space. To the best of our knowledge, these are the first such estimates without assuming smallness of first derivatives of the defining map. An immediate application is a convergence theorem of the mean curvature flow of the graph of an area decreasing map between flat Riemann surfaces.

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