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arXiv · 2609.15599

On the uniform flatness of polynomial graphs

Xieping Wang·Li Zhang
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Abstract

This paper grew out of an effort to understand the so-called uniform flatness, an important concept in the Bargmann--Fock interpolation theory developed by Varolin et al. We show that the graph of every polynomial in one complex variable is a uniformly flat algebraic curve in $\mathbb C^2$, with vanishing upper density with respect to the Gaussian weight. Combined with a result of Pingali and Varolin, this implies that such graphs are interpolating for the Bargmann--Fock space on $\mathbb C^2$.

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Xieping Wang, Li Zhang. 2026-09-14. On the uniform flatness of polynomial graphs. https://doi.org/10.1112/blms.70253

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