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-Hershkov...

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In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.

alpha thalassemia (α-thal) is relatively common worldwide. most carriers are defective in either one or two alpha globin genes out of four functional ones, with deletions being more common than point mutations. the hematologic features are very important for the selection of the appropriate molecular tests while determining the genotype. the aim of this study was to compare hematologic features...