Global Existence of a Mean Curvature Flow in a Cone (Journal of Mathematical Study, 2024)
We consider a mean curvature flow in a cone, that is, a hypersurface in acone which propagates toward the opening of the cone with normal velocity depending on its mean curvature. In addition, the contact angle between the hypersurface andthe cone boundary depending on its position. First, we construct a family of radiallysymmetric self-similar solutions. Then we use these solutions to give a priori estimatesfor the solutions of the initial boundary value problems, and show their global existence.