In R^3, Lipschitz continuous viscosity solutions to the K-prescribed Levi curvature equation are smooth and strictly pseudoconvex if K is smooth and strictly positive; see [5]. We show here that in R^2n+1, n > 1, a similar result does not hold; that is, we prove the existence in C^n+1, n > 1, of nonsmooth pseudoconvex hypersurfaces with smooth Levi curvature.
Nonsmooth hypersurfaces with smooth Levi curvature
LANCONELLI, ERMANNO;MONTANARI, ANNAMARIA
2013
Abstract
In R^3, Lipschitz continuous viscosity solutions to the K-prescribed Levi curvature equation are smooth and strictly pseudoconvex if K is smooth and strictly positive; see [5]. We show here that in R^2n+1, n > 1, a similar result does not hold; that is, we prove the existence in C^n+1, n > 1, of nonsmooth pseudoconvex hypersurfaces with smooth Levi curvature.File in questo prodotto:
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