Abstract
The gradient flow of the surface functional of compact hypersurfaces with respect to the inner product of L 2 is described by the evolution of surfaces by their mean curvature. This type of flows have been studied using methods from differential geometry and the theory of partial differential equations as well. In this paper we are interested in the evolution of surfaces obtained by rotating the graph of a positive and periodic function around the abscissa. The main result of this work completes the studies presented in [2] and [5]. More precisely, we prove that for periodic surfaces with non-negative mean curvature satisfying a natural monotonicity property the solution to the mean curvature flow blows up in finite time in the sense that neck pinching occurs.
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