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We give partial boundary regularity for co-dimension one absolutelyarea-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 withconstant orientation vector; this partial regularity is such that we canconclude the tangent cone is unique. The proof follows closely the boundaryregularity result given by Hardt and Simon in [9].

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