Details
| Original language | English |
|---|---|
| Pages (from-to) | 849-883 |
| Number of pages | 35 |
| Journal | Mathematische Zeitschrift |
| Volume | 240 |
| Issue number | 4 |
| Publication status | Published - 1 Aug 2002 |
| Externally published | Yes |
Abstract
We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle α for the corresponding Lagrangian submanifold in the cross product space L ⊂ M satisfies osc(α) ≤ π. If one considers a 4-dimensional Kähler-Einstein manifold M̄ of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that L ⊂ M̄ is a compact oriented Lagrangian submanifold w.r.t. J such that the Kähler form k̄ w.r.t. K restricted to L is positive and osc(α) ≤ π, then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. k̄.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Zeitschrift, Vol. 240, No. 4, 01.08.2002, p. 849-883.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Angle theorems for the lagrangian mean curvature flow
AU - Smoczyk, Knut
PY - 2002/8/1
Y1 - 2002/8/1
N2 - We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle α for the corresponding Lagrangian submanifold in the cross product space L ⊂ M satisfies osc(α) ≤ π. If one considers a 4-dimensional Kähler-Einstein manifold M̄ of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that L ⊂ M̄ is a compact oriented Lagrangian submanifold w.r.t. J such that the Kähler form k̄ w.r.t. K restricted to L is positive and osc(α) ≤ π, then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. k̄.
AB - We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle α for the corresponding Lagrangian submanifold in the cross product space L ⊂ M satisfies osc(α) ≤ π. If one considers a 4-dimensional Kähler-Einstein manifold M̄ of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that L ⊂ M̄ is a compact oriented Lagrangian submanifold w.r.t. J such that the Kähler form k̄ w.r.t. K restricted to L is positive and osc(α) ≤ π, then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. k̄.
UR - http://www.scopus.com/inward/record.url?scp=0035982247&partnerID=8YFLogxK
U2 - 10.1007/s002090100402
DO - 10.1007/s002090100402
M3 - Article
AN - SCOPUS:0035982247
VL - 240
SP - 849
EP - 883
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 4
ER -