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Research Report MRR00-029
Weingarten Hypersurfaces with Prescribed Gradient Image
John Urbas
Abstract:
We prove the existence of globally smooth convex solutions $u$ of a class
of curvature equations subject to the boundary condition
$Du(\Omega)=\Omega^*$ where $\Omega$ and $\Omega^*$ are smooth uniformly
convex domains in $R^n$. The results generalize some of our previous work
on the two dimensional case, and on Hessian equations in all dimensions.
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