arXiv:2611.03716v1 Announce Type: new Abstract: We extend Brown's one-variable rigidity theorem to strictly convex functions of two variables under a regularity assumption. Let $K\subset\mathbb{R}^2$ be nonempty, compact, and convex, and let $f$ be real-valued, strictly convex on $K$, and of class $C^2$ on a neighbourhood of $K$. We prove that the generating set $\{x_1,x_2,f\}$ is hyperrigid in $C(K)$.
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