Uniqueness of boundary tangent cones for 2-dimensional area-minimizing currents

2021/11/04 by Camillo De Lellis, De Lellis, Camillo, Stefano Nardulli +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.2111.02981

9 pages, 2 figures

arxiv created 2021/11/04 · openalex publication_date 2021/11/04 · arxiv updated 2021/11/05 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper we show that, if T is an area-minimizing 2-dimensional integral current with ∂ T = Q [ [ Γ] ], where Γ is a C^1,α curve for α>0 and Q an arbitrary integer, then T has a unique tangent cone at every boundary point, with a polynomial convergence rate. The proof is a simple reduction to the case Q=1, studied by Hirsch and Marini.

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