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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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


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
  • Email:
  • 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
  • MR Author ID: 278086
  • Email:
  • Mu-Tao Wang
  • Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
  • MR Author ID: 626881
  • Email:
  • 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.
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 7763-7775
  • MSC (2010): Primary 53C44
  • DOI:
  • MathSciNet review: 3546783