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- W3211686985 abstract "For convex hypersurfaces in the affine space $mathbb{A}^{n+1}$ ($ngeq2$), A.-M. Li introduced the notion of $alpha$-normal field as a generalization of the affine normal field. By studying a Monge-Amp`ere equation with gradient blowup boundary condition, we show that regular domains in $mathbb{A}^{n+1}$, defined with respect to a proper convex cone and satisfying some regularity assumption if $ngeq3$, are foliated by complete convex hypersurfaces with constant Gauss-Kronecker curvature relative to the Li-normalization. When $n=2$, a key feature is that no regularity assumption is required, and the result extends our recent work about the $alpha=1$ case." @default.
- W3211686985 created "2021-11-22" @default.
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- W3211686985 date "2022-01-01" @default.
- W3211686985 modified "2023-09-25" @default.
- W3211686985 title "Hypersurfaces of constant Gauss-Kronecker curvature with Li-normalization in affine space" @default.
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