Soliton solutions of the mean curvature flow and minimal hypersurfaces

Details Soliton solutions of the mean curvature flow and minimal hypersurfaces Soliton solutions of the mean curvature flow and minimal hypersurfaces

2011-04-21

arxiv.org/abs/1104.4166v1

Proc. Amer. Math. Soc. 140 (2012), no. 6, 2117-2126

Mathematics

Differential Geometry

11 pages, 1 figure

Scientific paper

10.1090/S0002-9939-2011-11205-X

Let (M,g) be an oriented Riemannian manifold of dimension at least 3 and X a vector field on M. We show that the Monge-Amp\`ere differential system (M.A.S.) for X-pseudosoliton hypersurfaces on (M,g) is equivalent to the minimal hypersurface M.A.S. on (M,g') for some Riemannian metric g', if and only if X is the gradient of a function u, in which case g'=exp(-2u)g. Counterexamples to this equivalence for surfaces are also given.

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