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...

the crisis of the religios legitimacy of safavids close to the end of this dynasty’s governance triggered many uprisings and rebellions in different parts of their ruling domain. sheikh baha_al_din estiri was the leader of one of the most important uprisings in khorasan. the sheikh, who has been frustrated with the safavid court and government’s indifference regarding the ozbacks’ attacks made ...

An abstract is not available for this content so a preview has been provided. Please use the Get access link above information on how to content.

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.