## Mean curvature flow of contractions between Euclidean spaces

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We consider the mean curvature flow of the graphs of maps between Euclidean spaces of arbitrary dimension. If the initial map is Lipschitz and satisfies a length-decreasing condition, we show that the mean curvature flow has a smooth long-time solution for t> 0. Further, we prove uniform decay estimates for the mean curvature vector and for all higher-order derivatives of the defining map.

Originalsprog Engelsk 104 Calculus of Variations and Partial Differential Equations 55 4 0944-2669 https://doi.org/10.1007/s00526-016-1043-2 Udgivet - 1 aug. 2016 Ja

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