Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 25-46 |
Seitenumfang | 22 |
Fachzeitschrift | Calculus of Variations and Partial Differential Equations |
Jahrgang | 20 |
Ausgabenummer | 1 |
Publikationsstatus | Veröffentlicht - 1 Mai 2004 |
Extern publiziert | Ja |
Abstract
Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform C2,α-bounds in space and C 2-estimates in time for the underlying Monge-Ampère equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the 2-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Calculus of Variations and Partial Differential Equations, Jahrgang 20, Nr. 1, 01.05.2004, S. 25-46.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Longtime existence of the Lagrangian mean curvature flow
AU - Smoczyk, Knut
PY - 2004/5/1
Y1 - 2004/5/1
N2 - Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform C2,α-bounds in space and C 2-estimates in time for the underlying Monge-Ampère equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the 2-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.
AB - Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform C2,α-bounds in space and C 2-estimates in time for the underlying Monge-Ampère equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the 2-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.
UR - http://www.scopus.com/inward/record.url?scp=2142715277&partnerID=8YFLogxK
U2 - 10.1007/s00526-003-0226-9
DO - 10.1007/s00526-003-0226-9
M3 - Article
AN - SCOPUS:2142715277
VL - 20
SP - 25
EP - 46
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 1
ER -