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Transactions of the American Mathematical Society

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Curvature decay estimates of graphical mean curvature flow in higher codimensions

Authors: Knut Smoczyk, Mao-Pei Tsui and Mu-Tao Wang
Journal: Trans. Amer. Math. Soc. 368 (2016), 7763-7775
MSC (2010): Primary 53C44
Published electronically: January 26, 2016
MathSciNet review: 3546783
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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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Additional Information

Knut Smoczyk
Affiliation: Institut für Differentialgeometrie and Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

Mao-Pei Tsui
Affiliation: Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan – and– Department of Mathematics and Statistics, University of Toledo, 2801 W. Bancroft Street, Toledo, Ohio 43606-3390

Mu-Tao Wang
Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027

Keywords: Mean curvature flow
Received by editor(s): January 23, 2014
Received by editor(s) in revised form: November 28, 2014
Published electronically: January 26, 2016
Additional Notes: The first author was supported by the DFG (German Research Foundation)
The second author was partially supported by a Collaboration Grant for Mathematicians from the Simons Foundation, #239677.
The third author was partially supported by National Science Foundation grants DMS 1105483 and DMS 1405152.
Article copyright: © Copyright 2016 American Mathematical Society

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