Author

C. Demeter

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Preprint Sep 2026

Diameter-free reverse inequalities and superorthogonality

We prove three results as part of the program of diameter-free estimates initiated in [CDW26]. The first two are reverse square function estimates for the light cone in $\mathbb{R}^3$. We first establish an abstract $L^4$ inequality of independent interest, under an ordered superorthogonality hypothesis: for every four...

A. Cushman, C. Demeter, Shu-Kun Wu · 0 citations

Preprint Aug 2026

Near optimal three-fold additive energy bound for points on convex curves

Let $X\subset\mathbb{R}$ be finite and let $\gamma(t)=(t,f(t))$, where $f$ is strictly convex. We show that \[ J_3(\gamma(X)) =\#\{(x_1,\ldots,x_6)\in X^6:\sum_{i=1}^3\gamma(x_i)=\sum_{i=4}^6\gamma(x_i)\} \ll_{\epsilon}|X|^{3+\epsilon}. \] When specialized to the parabola, our result implies near-optimal estimates for...

Adam Cushman, C. Demeter, Shu-Kun Wu · 5 citations · ⚡1