Desingularization of branch points of minimal disks in $\mathbb{R}^4$

TL;DR

This paper presents a method to deform minimal disks in four-dimensional space with branch points into symplectic minimal disks that only have transverse double points, simplifying their singularities.

Contribution

It introduces a novel deformation technique that replaces branch points with transverse double points in minimal disks within -dimensional space.

Findings

Branch points can be smoothed into transverse double points.

Deformation preserves minimality and symplectic structure.

Method provides new insights into the topology of minimal surfaces.

Abstract

We deform a minimal disk in $\mathbb{R}^4$ with a branch point into symplectic minimally immersed disks with only transverse double points.