Details
| Original language | English |
|---|---|
| Article number | e13000 |
| Number of pages | 33 |
| Journal | Journal of the London Mathematical Society |
| Volume | 110 |
| Issue number | 5 |
| Publication status | Published - 10 Oct 2024 |
Abstract
We consider the graphical mean curvature flow of maps (Formula presented.), (Formula presented.), and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well-known maximum principle of Ecker and Huisken derived in their seminal paper [Ann. of Math. (2) 130:3(1989), 453–471]. In the case of uniformly area decreasing maps (Formula presented.), (Formula presented.), we use this maximum principle to show that the graphicality and the area decreasing property are preserved. Moreover, if the initial graph is asymptotically conical at infinity, we prove that the normalized mean curvature flow smoothly converges to a self-expander.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Journal of the London Mathematical Society, Vol. 110, No. 5, e13000, 10.10.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Codimension two mean curvature flow of entire graphs
AU - Savas Halilaj, Andreas
AU - Smoczyk, Knut
N1 - Publisher Copyright: © 2024 The Author(s). Journal of the London Mathematical Society is copyright © London Mathematical Society.
PY - 2024/10/10
Y1 - 2024/10/10
N2 - We consider the graphical mean curvature flow of maps (Formula presented.), (Formula presented.), and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well-known maximum principle of Ecker and Huisken derived in their seminal paper [Ann. of Math. (2) 130:3(1989), 453–471]. In the case of uniformly area decreasing maps (Formula presented.), (Formula presented.), we use this maximum principle to show that the graphicality and the area decreasing property are preserved. Moreover, if the initial graph is asymptotically conical at infinity, we prove that the normalized mean curvature flow smoothly converges to a self-expander.
AB - We consider the graphical mean curvature flow of maps (Formula presented.), (Formula presented.), and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well-known maximum principle of Ecker and Huisken derived in their seminal paper [Ann. of Math. (2) 130:3(1989), 453–471]. In the case of uniformly area decreasing maps (Formula presented.), (Formula presented.), we use this maximum principle to show that the graphicality and the area decreasing property are preserved. Moreover, if the initial graph is asymptotically conical at infinity, we prove that the normalized mean curvature flow smoothly converges to a self-expander.
UR - http://www.scopus.com/inward/record.url?scp=85206256162&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2403.10739
DO - 10.48550/arXiv.2403.10739
M3 - Article
AN - SCOPUS:85206256162
VL - 110
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
SN - 0024-6107
IS - 5
M1 - e13000
ER -