Ancient Solutions of the Affine Normal Flow

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dc.creatorLoftin, John
dc.creatorTsui, Mao-Pei
dc.date2006-02-22
dc.date2006-07-31
dc.date.accessioned2026-07-07T07:03:41Z
dc.date.available2026-07-07T07:03:41Z
dc.descriptionWe construct noncompact solutions to the affine normal flow of hypersurfaces, and show that all ancient solutions must be either ellipsoids (shrinking solitons) or paraboloids (translating solitons). We also provide a new proof of the existence of a hyperbolic affine sphere asymptotic to the boundary of a convex cone containing no lines, which is originally due to Cheng-Yau. The main techniques are local second-derivative estimates for a parabolic Monge-Ampere equation modeled on those of Ben Andrews and Gutierrez-Huang, a decay estimate for the cubic form under the affine normal flow due to Ben Andrews, and a hypersurface barrier due to Calabi.
dc.descriptionA corrollary retracted, and a remark and some typos fixed
dc.identifierhttps://arxiv.org/abs/math/0602484
dc.identifierhttp://arxiv.org/abs/math/0602484
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109064
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53C44, 53A15
dc.titleAncient Solutions of the Affine Normal Flow
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