Partial boundary regularity for co-dimension one area-minimizing currents at immersed $C^{1,\alpha }$ tangential boundary points; full exposition

Abstract

We give partial boundary regularity for co-dimension one absolutely area-minimizing currents at points where the boundary consists of a sum of $C^{1,\alpha }$ 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.

arXiv comment82 pages. See arXiv:1508.04229v2 for an alternate abridged version