Details
| Original language | English |
|---|---|
| Pages (from-to) | 7763-7775 |
| Number of pages | 13 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 368 |
| Issue number | 11 |
| Publication status | Published - 1 Jan 2016 |
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.
Keywords
- Mean curvature flow
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics(all)
- Applied Mathematics
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In: Transactions of the American Mathematical Society, Vol. 368, No. 11, 01.01.2016, p. 7763-7775.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Curvature decay estimates of graphical mean curvature flow in higher codimensions
AU - Smoczyk, Knut
AU - Tsui, Mao Pei
AU - Wang, Mu Tao
N1 - Funding information: 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.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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.
AB - 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.
KW - Mean curvature flow
UR - http://www.scopus.com/inward/record.url?scp=84987788599&partnerID=8YFLogxK
U2 - 10.1090/tran/6624
DO - 10.1090/tran/6624
M3 - Article
AN - SCOPUS:84987788599
VL - 368
SP - 7763
EP - 7775
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 11
ER -