# Recent progress on the Dirichlet problem for the minimal surface system and minimal cones

## TL;DR

This paper reviews recent advances in solving the Dirichlet problem for minimal surface systems and the classification of minimal cones in high-dimensional Euclidean spaces, highlighting new results and ongoing challenges.

## Contribution

It summarizes recent developments on the Dirichlet problem for high-codimension minimal graphs and introduces new families of area-minimizing cones.

## Key findings

- Exploration of non-existence and non-uniqueness of solutions
- New constructions of minimal cones with various properties
- Advances in understanding irregularity in high codimension minimal surfaces

## Abstract

This is a very brief report on recent developments on the Dirichlet problem for the minimal surface system and minimal cones in Euclidean spaces. We shall mainly focus on two directions: (1) Further systematic developments after Lawson-Osserman's paper \cite{l-o} on the Dirichlet problem for minimal graphs of high codimensions. Aspects including non-existence, non-uniqueness and irregularity properties of solutions have been explored from different points of view. (2) Complexities and varieties of area-minimizing cones in high codimensions. We shall mention interesting history and exhibit some recent results which successfully furnished new families of minimizing cones of different types.