Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 849-883 |
| Seitenumfang | 35 |
| Fachzeitschrift | Mathematische Zeitschrift |
| Jahrgang | 240 |
| Ausgabenummer | 4 |
| Publikationsstatus | Veröffentlicht - 1 Aug. 2002 |
| Extern publiziert | Ja |
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 Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Mathematische Zeitschrift, Jahrgang 240, Nr. 4, 01.08.2002, S. 849-883.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -