Self-shrinkers of the mean curvature flow in arbitrary codimension

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dc.creatorSmoczyk, Knut
dc.date2005-07-15
dc.date.accessioned2026-07-07T05:21:45Z
dc.date.available2026-07-07T05:21:45Z
dc.descriptionFor hypersurfaces of dimension greater than one, Huisken showed that compact self-shrinkers of the mean curvature flow with positive scalar mean curvature are spheres. We will prove the following extension: A compact self-similar solution in arbitrary codimension and of dimension greater than one is spherical, i.e. contained in a sphere, if and only if the mean curvature vector \be H\ee is non-vanishing and the principal normal \beν\ee is parallel in the normal bundle. We also give a classification of complete noncompact self-shrinkers of that type.
dc.description19 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0507325
dc.identifierhttp://arxiv.org/abs/math/0507325
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75802
dc.subjectDifferential Geometry
dc.subject53C44
dc.titleSelf-shrinkers of the mean curvature flow in arbitrary codimension
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