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

2019/06/11 by Yongsheng Zhang, Zhang, Yongsheng · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Differential Geometry (math.DG) #FOS: Mathematics #Graph theory and applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1906.04558

openalex publication_date 2019/06/11 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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 \citel-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.

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• The Dirichlet problem for the minimal surface system on smooth domains

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