The Dirichlet problem for the minimal surface equation in \rm Sol₃, with possible infinite boundary data

2013/12/21 by Minh Nguyen, Nguyen, Minh Hoang
Computer Science · Mathematics · #53A10 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1312.6194

openalex publication_date 2013/12/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Dirichlet problem for the minimal surface equation in \rm Sol₃ with possible infinite boundary data, where \rm Sol₃ is the non-abelian solvable 3-dimensional Lie group equipped with its usual left-invariant metric that makes it into a model space for one of the eight Thurston geometries. Our main result is a Jenkins-Serrin type theorem which establishes necessary and sufficient conditions for the existence and uniqueness of certain minimal Killing graphs with a non-unitary Killing vector field in \rm Sol₃.

Citations

• Cylindrically bounded constant mean curvature surfaces in ℍ²×ℝ

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