Partial boundary regularity for co-dimension one area-minimizing currents at immersed C^1,α tangential boundary points; full exposition

2017/04/18 by Leobardo Rosales, Rosales, Leobardo
Computer Science · Mathematics · #28A75 #49Q05 #49Q15 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1704.05164

openalex publication_date 2017/04/18 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We give partial boundary regularity for co-dimension one absolutely area-minimizing currents at points where the boundary consists of a sum of C^1,α submanifolds, possibly with multiplicity, meeting tangentially, given that the current has a tangent cone supported in a hyperplane with constant orientation vector; this partial regularity is such that we can conclude the tangent cone is unique. The proof closely follows that giving the boundary regularity result of Hardt and Simon.

Related

• Partial boundary regularity for co-dimension one area-minimizing currents at immersed C^1,α tangential boundary points
• Co-Dimension One Area-Minimizing Currents with C^1,α Tangentially Immersed Boundary
• Co-dimension one area-minimizing currents with C^1,α tangentially immersed boundary having Lipschitz co-oriented mean curvature
• On the uniqueness of tangent cones to area minimizing currents at boundaries with arbitrary multiplicity
• An essential one sided boundary singularity for a 3-dimensional area minimizing current in ℝ⁵