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Minimal Lagrangian surfaces in ℂP^2 via the loop group method Part II: The general case

arxiv(2024)

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摘要
We extend the techniques introduced in for contractible Riemann surfaces to construct minimal Lagrangian immersions from arbitrary Riemann surfaces into ℂP^2 via the loop group method. Based on the potentials of translationally equivariant minimal Lagrangian surfaces, we introduce perturbed equivariant minimal Lagrangian surfaces in ℂP^2 and construct a class of minimal Lagrangian cylinders. Furthermore, we show that these minimal Lagrangian cylinders approximate Delaunay cylinders with respect to some weighted Wiener norm of the twisted loop group Λ SU(3)_σ.
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