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Longtime existence of the Lagrangian mean curvature flow

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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OriginalspracheEnglisch
Seiten (von - bis)25-46
Seitenumfang22
FachzeitschriftCalculus of Variations and Partial Differential Equations
Jahrgang20
Ausgabenummer1
PublikationsstatusVeröffentlicht - 1 Mai 2004
Extern publiziertJa

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.

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Longtime existence of the Lagrangian mean curvature flow. / Smoczyk, Knut.
in: Calculus of Variations and Partial Differential Equations, Jahrgang 20, Nr. 1, 01.05.2004, S. 25-46.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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