Author

Mingfeng Chen

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Preprint Sep 2026

Sharp $L^p$ estimates for the strong spherical maximal operator

We prove that the strong spherical maximal operator in $\mathbb{R}^n$ is bounded on $L^p$ for $n\geq4$ and $p>(n+1)/(n-1)$. This establishes the conjecture of Hickman and Zahl in the remaining dimensions. The main ingredient is a local $L^2$ estimate for the pieces obtained by a dyadic decomposition in the normal varia...

Ming-Feng Chen · 1 citation · ⚡1

Preprint Aug 2026

Sharp Bounds for Rational Points Near Space Curves

Let $Q\geq 1$ be large, and $\delta \in(0,1)$ be small. Denote by $\mathcal C \subset \mathbb R^3$ a sufficiently smooth curve with non-vanishing curvature and torsion. How many rational points $\mathbf{a}/q$ of height $q\in[1, Q]$ are $\delta/q$-near $\mathcal C$? This manuscript provides an essentially optimal answer...

Ming-Feng Chen, A. Seeger, Rajula Srivastava et al. · 3 citations