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- W2927304313 abstract "Let $X$ denote $mathbb{R}^n$ or, more generally, a Hilbert space. Given an arbitrary subset $C$ of $X$ and a collection $mathcal{H}$ of affine hyperplanes of $X$ such that every $Hinmathcal{H}$ passes through some point $x_{H}in C$, and $C={x_H : Hinmathcal{H}}$, what conditions are necessary and sufficient for the existence of a $C^{1,1}$ convex hypersurface $S$ in $X$ such that $H$ is tangent to $S$ at $x_H$ for every $Hinmathcal{H}$? In this paper we give an answer to this question. We also provide solutions to similar problems for convex hypersurfaces of class $C^{1, omega}$ in Hilbert spaces, and for convex hypersurfaces of class $C^{1, alpha}$ in superreflexive Banach spaces having equivalent norms with moduli of smoothness of power type $1+alpha$, $alphain (0, 1].$" @default.
- W2927304313 created "2019-04-11" @default.
- W2927304313 creator A5012686953 @default.
- W2927304313 creator A5023519092 @default.
- W2927304313 date "2019-04-07" @default.
- W2927304313 modified "2023-09-27" @default.
- W2927304313 title "Prescribing tangent hyperplanes to $C^{1,1}$ and $C^{1,omega}$ convex hypersurfaces in Hilbert and superreflexive Banach spaces" @default.
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