Remarks on "Spiral Minimal Products"

TL;DR

This paper discusses recent developments in minimal Lagrangian geometry, highlighting a generalized Delaunay construction and the discovery of numerous new special Lagrangian cones with various density properties.

Contribution

It provides a structural framework for minimal Lagrangians in complex projective spaces and identifies many new special Lagrangian cones with diverse density characteristics.

Findings

Generalized Delaunay construction for minimal Lagrangians

Existence of uncountably many new special Lagrangian cones

Identification of cones with finite and infinite density

Abstract

This note aims to give a better understanding and some remarks about recent preprint ``Spiral Minimal Products". In particular, 1. it should be pointed out that a generalized Delaunay construction among minimal Lagrangians of complex projective spaces has been set up. This is a general structural result working for immersion and current situations. 2. uncountably many new regular (or irregular) special Lagrangian cones with finite density and ``regular" (or irregular) special Lagrangian cones with infinite density in complex Euclidean spaces can be found.