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Evolution of convex entire graphs by curvature flows

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Alessandroni R., Sinestrari C.

Geometric Flows

2015

tom 1

nr 1

We consider the evolution of an entire convex graph in euclidean space with speed given by a symmetric function of the principal curvatures. Under suitable assumptions on the speed and on the initial data, we prove that the solution exists for all times and it remains a graph. In addition, after appropriate rescaling, it converges to a homothetically expanding solution of the flow. In this way, we extend to a class of nonlinear speeds the well known results of Ecker and Huisken for the mean curvature flow.

Ograniczanie wyników

1 Geometric Flows

1 Alessandroni R.

1 Sinestrari C.

1 2015

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Evolution of convex entire graphs by curvature flows