Mean Convex Mean Curvature Flow with Free Boundary

In this paper, we generalize White's regularity and structure theory for mean-convex mean curvature flow [45, 46, 48] to the setting with free boundary. A major new challenge in boundary is derive an a priori bound ratio between norm of second fundamental form curvature. We establish such via maximum principle triple-approximation scheme, which combines ideas from Edelen [9], Haslhofer-Hershkovits [16], Volkmann [43]. Other important ingredients are Bernstein-type theorem sheeting low-entropy flows half-slab, allow us rule out multiplicity 2 (half-)planes as possible tangent and, domains, limit flows. © 2021 Wiley Periodicals LLC.