Uniqueness of tangent cones to boundary points of two-dimensional almost-minimizing currents

2019/09/29 by Jonas Hirsch, Michele Marini, Hirsch, Jonas +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1909.13383

arxiv created 2019/09/29 · arxiv updated 2019/10/01

Abstract

We prove that tangent cones at singular boundary points of a two-dimensional current almost area minimizing are unique. Following the ideas exposed by White in [8], the result is achieved by combining a suitable epiperimetric inequality and an almost-monotonicity formula for the mass at boundary points.

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