Consistency of minimizing movements with smooth mean curvature flow of droplets with prescribed contact angle in $$\mathbb {R}^3$$

Abstract In this paper we prove that in $$\mathbb {R}^3$$ the minimizing movement solutions for mean curvature motion of droplets, obtained in Bellettini (JMPA 117:1–58, 2018), coincide with the smooth mean curvature flow of droplets with a prescribed (possibly nonconstant) contact angle.