Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

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
DOI: https://doi.org/10.1090/tran/6624
Published electronically: January 26, 2016
MathSciNet review: 3546783
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 53C44

Retrieve articles in all journals with MSC (2010): 53C44


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
Email: mao-pei.tsui@utoledo.edu

Mu-Tao Wang
Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
Email: mtwang@math.columbia.edu

DOI: https://doi.org/10.1090/tran/6624
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