Allard-Type Regularity for Varifolds with Prescribed Contact Angle

Given a bounded C² domain in Rⁿ⁺¹ and an integral n-rectifiable varifold V with bounded first variation and bounded generalized mean curvature. Given a C¹ function θ defined on the boundary of the domain with range (0,π), we assume V has prescribed contact angle θ with ∂ Ω and the tangent cone of V at a point X ∈ ∂ Ω is a half-hyperplane of density one. Then we can show that the support of V is a C1,γ hypersurface with boundary near X for some γ ∈ (0,1).