Applications of current-varifold pair to variational method

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I have been studying a mathematical model describing phase separation phenomena for the past 15 years. Through the analysis of such model, I realized the importance of a viewpoint to consider surface orientation and surface measure as a pair. In particular, I obtain such a pair as a limiting object when I consider a singular perturbation problem of mean curvature flow. Using this characteristic, I am able to obtain some existence and regularity theorems. The examples of my theorems are existence and regularity theory of mean curvature flow with transport term (joint work with Keisuke Takasao, in review) and existence theorem and characterization of boundary condition of mean curvature flow on a convex domain with Neumann condition (joint work with Masashi Mizuno, in review).