## 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.## References

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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: smoczyk@math.uni-hannover.de
**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: mao-pei.tsui@utoledo.edu
**Mu-Tao Wang**- Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
- MR Author ID: 626881
- Email: mtwang@math.columbia.edu
- 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: https://doi.org/10.1090/tran/6624
- MathSciNet review: 3546783