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.
@article{bwmeta1.element.doi-10_1515_geofl-2015-0006,
author = {Roberta Alessandroni and Carlo Sinestrari},
title = {Evolution of convex entire graphs by curvature flows},
journal = {Geometric Flows},
volume = {1},
year = {2015},
zbl = {1248.53047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_geofl-2015-0006}
}
Roberta Alessandroni; Carlo Sinestrari. Evolution of convex entire graphs by curvature flows. Geometric Flows, Tome 1 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_geofl-2015-0006/
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