On the evolution of convex hypersurfaces by the $Q_k$ flow

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dc.creatorCaputo, M. Cristina
dc.creatorDaskalopoulos, Panagiota
dc.creatorSesum, Natasa
dc.date2009-04-03
dc.date.accessioned2026-07-07T13:00:11Z
dc.date.available2026-07-07T13:00:11Z
dc.descriptionWe prove the existence and uniqueness of a $C^{1,1}$ solution of the $Q_k$ flow in the viscosity sense for compact convex hypersurfaces $Σ_t$ embedded in $R^{n+1}$ ($n \geq 2$) . In particular, for compact convex hypersurfaces with flat sides we show that, under a certain non-degeneracy initial condition, the interface separating the flat from the strictly convex side, becomes smooth, and it moves by the $Q_{k-1}$ flow at least for a short time.
dc.identifierhttps://arxiv.org/abs/0904.0492
dc.identifierhttp://arxiv.org/abs/0904.0492
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225781
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.titleOn the evolution of convex hypersurfaces by the $Q_k$ flow
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