Preprint 31/2001

Angle theorems for the Lagrangian mean curvature flow

Knut Smoczyk

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Submission date: 26. May. 2001
Pages: 33
published in: Mathematische Zeitschrift, 240 (2002) 4, p. 849-883 
DOI number (of the published article): 10.1007/s002090100402
MSC-Numbers: 53C44

We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive curvature converge to minimal symplectic maps, if the Lagrangian angle tex2html_wrap_inline12 for the corresponding Lagrangian submanifold in the cross product space tex2html_wrap_inline14 satisfies tex2html_wrap_inline16. If one considers a 4-dimensional Kähler-Einstein manifold tex2html_wrap_inline20 of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that tex2html_wrap_inline24 is a compact oriented Lagrangian submanifold w.r.t. J such that the Kähler form tex2html_wrap_inline28 w.r.t. K restricted to L is positive, then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. tex2html_wrap_inline28.

24.11.2021, 02:11