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

Abstract

In this paper, we employ the loop group method to study the construction of minimal Lagrangian surfaces in the complex projective plane for which the surface is contractible. We present several new classes of minimal Lagrangian surfaces in $\mathbb{C}{P}^2$.

45 pages

References in corpus (5)

• The geometric complexity of special Lagrangian $T^2$-cones
• Equivariant harmonic cylinders
• The Novikov-Veselov hierarchy of equations and integrable deformations of minimal Lagrangian tori in CP^2
• Triviality of the dressing isotropy for a Smyth-type potential and nonclosing of the resulting CMC surfaces
• Explicit expressions for the Iwasawa factors, the metric and the monodromy matrices for minimal Lagrangian surfaces in $\mathbb{C}{P}^2$

Cited by in corpus (1)

• Minimal Lagrangian surfaces in the two dimensional complex quadric via the loop group method