Qualitative Study On The Mean Curvature Flow Equation In A Cone

In the research field of mean curvature flow equations,for the equations about closed plane curves and closed surfaces in higher dimension spaces,there have been quite complete studies since 1980.This kind of problem has been extensively studied in sector domain.In this paper,we consider mean curvature flow equation with anisotropy coefficient in a cone.First,we construct a family of self-similar solutions by constructing auxiliary problem,using shooting method and Cantor's diagonal,then we straighten the boundary to prove global existence for the solution of problem.