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

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

2009-04-03

arxiv.org/abs/0904.0492v1

Mathematics

Analysis of PDEs

Scientific paper

We prove the existence and uniqueness of a $C^{1,1}$ solution of the $Q_k$ flow in the viscosity sense for compact convex hypersurfaces $\Sigma_t$ 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.

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