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arXiv · 2405.03246

Minimal Lagrangian surfaces in $\mathbb{C}P^2$ via the loop group method Part II: The general case

Josef F. Dorfmeister·Hui Ma
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Abstract

We extend the techniques introduced in \cite{DoMaB1} for contractible Riemann surfaces to construct minimal Lagrangian immersions from arbitrary Riemann surfaces into $\mathbb{C}P^2$ via the loop group method. Based on the potentials of translationally equivariant minimal Lagrangian surfaces, we introduce perturbed equivariant minimal Lagrangian surfaces in $\mathbb{C}P^2$ 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 $\Lambda SU(3)_{\sigma}$.

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Josef F. Dorfmeister, Hui Ma. 2024-05-06. Minimal Lagrangian surfaces in $\mathbb{C}P^2$ via the loop group method Part II: The general case. https://arxiv.org/abs/2405.03246

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