Uniqueness of boundary tangent cones for 2-dimensional area-minimizing currents. (May 2023)

• Record Type: Journal Article
• Authors: De Lellis, Camillo; Nardulli, Stefano; Steinbrüchel, Simone
• Is Part Of: Nonlinear analysis. Volume 230(2023)
• Publication Date: 2023-05
• Subjects: Area minimizing currents -- Regularity theory -- Boundary; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2023.113235
• Languages: English
• ISSNs: 0362-546X

Abstract

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 (2019).