Recent progress on the Dirichlet problem for the minimal surface system and minimal cones
Differential Geometry
2019-06-20 v2
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.
Cite
@article{arxiv.1906.04558,
title = {Recent progress on the Dirichlet problem for the minimal surface system and minimal cones},
author = {Yongsheng Zhang},
journal= {arXiv preprint arXiv:1906.04558},
year = {2019}
}