Curvature varifolds with orthogonal boundary

Abstract We consider the class of ‐dimensional surfaces in that intersect orthogonally along the boundary. A piece of an affine ‐plane in is called an orthogonal slice. We prove estimates for the area by the integral of the second fundamental form in three cases: first, when admits no orthogonal slices, second for if all orthogonal slices are topological disks, and finally, for all if the surfaces are confined to a neighborhood of . The orthogonality constraint has a weak formulation for curvature varifolds. We classify those varifolds of vanishing curvature. As an application, we prove for any the existence of an orthogonal 2‐varifold that minimizes the curvature in the integer rectifiable class.