Details
| Original language | English |
|---|---|
| Pages (from-to) | 243-257 |
| Number of pages | 15 |
| Journal | Journal of differential geometry |
| Volume | 62 |
| Issue number | 2 |
| Publication status | Published - 1 Jan 2002 |
| Externally published | Yes |
Abstract
This article studies the mean curvature flow of Lagrangian submanifolds. In particular, we prove the following global existence and convergence theorem: if the potential function of a Lagrangian graph in T2n is convex, then the flow exists for all time and converges smoothly to a flat Lagrangian submanifold. We also discuss various conditions on the potential function that guarantee global existence and convergence.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Geometry and Topology
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of differential geometry, Vol. 62, No. 2, 01.01.2002, p. 243-257.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Mean curvature flows of lagrangian submanifolds with convex potentials
AU - Smoczyk, Knut
AU - Wang, Mu Tao
PY - 2002/1/1
Y1 - 2002/1/1
N2 - This article studies the mean curvature flow of Lagrangian submanifolds. In particular, we prove the following global existence and convergence theorem: if the potential function of a Lagrangian graph in T2n is convex, then the flow exists for all time and converges smoothly to a flat Lagrangian submanifold. We also discuss various conditions on the potential function that guarantee global existence and convergence.
AB - This article studies the mean curvature flow of Lagrangian submanifolds. In particular, we prove the following global existence and convergence theorem: if the potential function of a Lagrangian graph in T2n is convex, then the flow exists for all time and converges smoothly to a flat Lagrangian submanifold. We also discuss various conditions on the potential function that guarantee global existence and convergence.
UR - http://www.scopus.com/inward/record.url?scp=0041657280&partnerID=8YFLogxK
U2 - 10.4310/jdg/1090950193
DO - 10.4310/jdg/1090950193
M3 - Article
AN - SCOPUS:0041657280
VL - 62
SP - 243
EP - 257
JO - Journal of differential geometry
JF - Journal of differential geometry
SN - 0022-040X
IS - 2
ER -