The symmetric `doughnut' evolving by its mean curvature
The author investigates flows of immersed manifolds \(M_ t\) in \(\mathbb{R}^{m+1}\) governed by their mean curvatures. The case of symmetric ``doughnuts'' \(M_ t\) is under consideration as well as the ``generating manifolds'' \(C_ t\) defined as intersections of \(M_ t\) with the half space \(\mathbb{R}^ m>0\). Existence of those families, their convergence and some other properties are established.
scientific article; zbMATH DE number 720803